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1
Toast the chilhuacle, ancho, and guajillo chiles on a dry comal or heavy skillet over medium heat, pressing each flat for a few seconds per side, until the skins blister and the flesh turns fragrant without scorching. Transfer immediately to a bowl of hot water and soak until fully softened, approximately 20–30 minutes. The chiles are ready when the flesh yields completely under pressure and the soaking water has turned a deep rust-red.
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2
Drain the soaked chiles, reserving the soaking liquid. Blend the chiles with enough of the soaking liquid to form a smooth, cohesive purée. Pass through a fine-mesh strainer, pressing firmly to extract all liquid and discard the skins and seeds. The strained base should run freely and coat the back of a spoon in a thin, even layer — this is the structural liquid of the stew, not a sauce.
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3
Pour the strained chile base into a large, heavy pot. Add 1.5 litres of water and bring to a moderate simmer over medium heat. Add the goat hip, ribs, and offal directly into the chile liquid. This is where the dish lives or dies: the bone, connective tissue, and fat of a freshly slaughtered seasonal animal must dissolve slowly into the broth over 2–3 hours of unhurried simmering — rushing this step prevents the collagen from fully extracting, and the characteristic mineral body of the stew will not develop. The broth is ready at this stage when the hip and rib meat begins to yield at the joint but has not yet fallen free.
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4
Add the hierba santa leaves to the pot. Continue to simmer, allowing the herb to perfume the broth. After 10–15 minutes, add the epazote sprigs. The two herbs are added at different times so that hierba santa's anise character permeates the liquid before epazote's sharper, more volatile oils are introduced. The broth is ready when both herbs have fully wilted and the liquid smells layered — goat fat, dried chile, and herb in equal measure.
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5
Season with salt. Ladle into deep bowls, ensuring each portion receives hip meat, rib, and a portion of offal. Serve with fresh tortillas and dried chile on the side, as is traditional.