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1
In a dry comal or heavy skillet over medium heat, toast the ancho, mulato, and guajillo chiles in batches, pressing each briefly with a spatula until fragrant and the skin blisters lightly. Transfer immediately to a bowl of hot water and soak for 20–30 minutes. The chiles are ready when the flesh is fully pliable and the soaking water is dark.
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2
Drain the soaked chiles. Transfer to a blender with the cumin, cinnamon, cloves, and tomatoes (or a measured splash of vinegar). Blend to a completely smooth paste, adding a little soaking water as needed. Pass through a medium-mesh strainer, pressing with the back of a spoon; discard solids. The strained paste should be fluid, uniform, and deep brick-red.
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3
This is where the dish lives or dies. In a wide, heavy pot melt the lard over high heat until it shimmers. Add the strained chile paste all at once — it will hiss violently. Stir constantly and fry the paste in the hot lard for 8–12 minutes, until it darkens by one clear shade, pulls away from the sides of the pot, and the raw, sharp smell gives way to something deeper, toasted, and complex. Skipping or shortening this step produces a flat, raw-tasting sauce.
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4
Add the pork shoulder pieces directly to the pot and turn to coat in the fried chile paste. Add enough of the reserved soaking water (or plain water) to partially submerge the meat. Bring to a simmer, cover, and braise over low heat, stirring occasionally. The braise is done when the pork yields completely to a fork and the sauce has reduced to a glossy, clingy consistency that coats the back of a spoon.
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5
Taste the sauce. Adjust salt. If the richness dominates, add a small amount of vinegar or orange juice to restore balance. The finished sauce should be bold and aromatic — cumin and cloves clearly present — with the brick-red colour confirming the correct chile balance: too brown suggests insufficient ancho; too orange, insufficient mulato.