If nothing exists independently, in what sense does anything exist at all?
The Middle Way runs between two errors. One says things exist solidly and independently, in their own right — the technical term is svabhāva, intrinsic existence, existence from a thing's own side. The other says that since they do not, nothing really exists and nothing much matters.
Madhyamaka rejects both, and the difficulty is that the correct position sounds, on a first hearing, exactly like the second error. This is why it is taught in year eleven and not year one.
The root text is Candrakīrti's Supplement to the Middle Way (Madhyamakāvatāra), a seventh-century work that follows Nāgārjuna's reasoning and defends the strictest reading of it — the Consequence school, Prāsaṅgika, which holds that the correct response to a mistaken position is to draw out its consequences rather than to advance a thesis of one's own.
Years thirteen and fourteen are given to Tsongkhapa's Illumination of the Thought, the commentary that fixed how this school is read in the Gelug tradition, and which is careful to insist that emptiness does not undermine ordinary things — it explains how they can work.
A monk can produce a correct definition of emptiness in his second year. It will not mean anything.
What debate does is expose the residue — the places where someone who can state the position still, in practice, treats things as existing from their own side. The courtyard finds this by pressing: if that were so, what would follow? The consequences are where the mistake shows.
This is the subject where the pedagogy and the content are the same shape. The Consequence school argues by drawing out implications; so does the courtyard.
The tradition does not treat this as metaphysics for its own sake. The claim is that grasping at things — including at oneself — as solid and independent is what generates the whole apparatus of craving and aversion, and that seeing through it is what loosens the grip.
Four years, on one question. It is the intellectual heart of the curriculum, and it connects directly to what the monastery means by meditation: analysis carried far enough to change how things look.
Back to education and intellectual training, or on to the other treatises: Pramāṇa, Prajñāpāramitā, Madhyamaka, Abhidharma, Vinaya.