It's very simple:
"Where this exists, that exists. With the arising of that, this arises...."
Since we cannot in the end find anything but appearances that are found on examination to be empty, all we are left with is appearances that arise in dependence upon other appearances...
It is axiomatic in Buddhadharma that there are no first causes. The very notion of pratītyasamutpada forbids the notion of any first cause, or creator, etc.
I already explained this: the basis of imputation is an appearance. Some trends on Madhyamaka then assert that appearances are mind. Since appearances/mind are not findable on analysis, they/it are equated with illusion. Illusions lack any inherent nature because they are dependent originations. Dependent originations are free from extremes and, in the final analysis, inexpressible. None of this is circular in anyway.
You ask, what dependently arises -- we can say all kinds of things, but in the end, it boils down to appearance. What are appearances? Dependent arisings. What dependently arises? Appearances. This is not a circularity, it is an equation appearances = dependent origination.
If you want to be more specific you can say what appearance? A rope or a car, for example. Upon what is a rope designated? It's parts. Upon what are the parts designated? Their parts, if they have any. If they do not have further parts, then they are designated upon moments, etc., until one runs out of bases of imputation. At that point, you have [intellectually] discovered emptiness, i.e., the absence of a ultimate or final basis of designation. At each stage of the analysis the previous basis of imputation no longer appears since it is has been deconstructed. As Shantideva points out:
When an existent or a nonexistent
does not exist in the presence of the mind,
at that time since there is no other aspect
[concepts] are fully pacified as there is no objective support [dmigs pa, ālambana].
...The arising of appearances needs to explained in some way, hence MMK 1.1
At no time, nowhere
do things arise from self,
or without a cause.
Madhyamaka serves to pacify proliferation through demonstrating dependent origination. This is the mangalaṃ of MMK states that dependent origination, unceasing, non-arising, etc., is the pacification of proliferation.
From your given appearance, one might explain appearances arise causelessly [Carvaka], or from themselves [Saṃkhya], from other [Vaiṣeśika], etc.
Nāgārjuna's project is twofold: one, to show that accounts of apparent phenomena other than dependent origination are unintelligible. Two, to show that dependently originated phenomena are empty.
He does this because of the subject/predicate [dharmin/dharmatā] problem in discussing phenomena in terms of essences. The dharmin in this case is appearances which are dependently arisings. When their predicate is sought, their dharmatā, it is found to be emptiness.
Since phenomena are found to be essenceless, they are likened to appearances that everyone accepts are unreal, i.e. illusions, apparitions, space and so on.
The Madhyamaka project is to show that as long as one insists that there is an ultimate basis of imputation beyond mere appearances, for that long one will be locked into conceptuality. Since in the final analysis, one can find no basis of imputation at all, and since the object under analysis ceases to appear as either an existent or in this case as a non-existent (since a non-existent cannot be predicated without an existent), one ceases to conceive of things as existents or nonexistents. That is the desiderata.
In the end it is very simple, this appearance, for example a sprout, depends on the appearance of that appearance, for example a seed; without the seed there is no sprout. This appearance, butter, depends on that appearance, milk., etc.
Dependent origination serves to explain causal processes without invoking essences. Dependent origination is something one can witness with one's own eyes, so in that sense it is not imputation, it is how things exist. In other words, at no time has anyone ever witnessed the arising of something that did not depend on a cause.
It is worthwhile here to repost the master's own words from his own magnum opus, Prasannapāda:
Therefore, that being the case, here when the Bhagavan [the Buddha] clarified the production of things depending on cause and condition, he refuted the production of things causelessly, from a single cause, a dissimilar cause, or generated by self and other. Since those were refuted, the intrinsic nature of relative things was taught according to how they exist relatively.
Please compare this with what I stated above:
Conventionally or relatively speaking, Candra[kirti] eliminates arising without a cause, from single causes, dissimilar causes or from self or other, leaving only arising from conditions as the only valid option.
It's pretty clear from Candra's language that there should be an object to be seen correctly or falsely. This means there must be an appearance about which one is either mistaken or unmistaken. When one unmistakenly sees the apparent objects which serves as the basis for imputation (hearkening back to your original qualm), depending on which strand of Tibetan Madhyamaka one is following:
a) the objects themselves do not actually arise in truth and are considered to be no more than illusions, and so on
the objects themselves arise from causes and conditions conventionally (i.e. not causelessly, from single causes, from self, other, or dissimilar causes). What objects do not do is arise inherently. [<--- Gelug POV]
Candra presupposes a Sautrantika epistemology where sense consciousnesses only arise when sense objects are encountered by contact with sense organs. For Candra, a sense consciousness will never arise in absence of a sense object or a sense organ, and this is clearly stated in the Madhyamakāvatara. Thus, the question of what the delusion actually is remains a matter of debate amongst Mādhyamika proponents...
...if we allow production from dissimilar causes we will have NO BASIS FOR REFUTING CREATION BY GOD. In that case, one will undermine the entire basis of Buddhadharma.
If you suggest that there can be production from dissimilar causes, a claim explicitly rejected in all Madhyamaka texts, you are allowing, for example, that unconditioned phenomena, for example God, can produce conditioned phenomena, for example, the world.
I also gave you the example of the production of maize from wheat seeds, chickens from cows and so on...
There is inexpressible and then there is inexpressible; how one arrives at inexpressibility is critical.
Hindus also claim that their ultimate is beyond predicates.
~ Loppon Namdrol [<--- a trained Sakya Loppon who can read/translate Sanskrit and Classical Tibetan]
"...In that case, one will undermine the entire basis of Buddhadharma", if one accepts the above conclusions of dependent origination, that too will undermine eternalist doctrines, and vice versa. If it's the case that someone does accept the above conclusons of dependent origination, then logically they could not accept phenomena arising from a first cause, dissimilar cause, from itself, etc. The dialectic of buddhadharma is airtight about this. Likewise, if someone accepted the arising of phenomena from a first cause and so on, then they could not logically accept the conclusions of dependent origination in buddhadharma. According to this scenario, a person cannot have his or her cake and eat it too; no "ifs, ands, or buts" about it. If a person is honest with themself, it would be evident that they could only logically accept the view of one or the other, since accepting the respective view of one premise contradicts and outright cancels the other premise, and vice versa.