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Preheat oven to 300°F with rack in middle.
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Put avocado leaves in bottom of a heavy medium pot with a tight-fitting lid. Sprinkle short ribs all over with 2 tsp salt and arrange in pot (it doesn’t have to be in 1 layer). Roast, covered, until meat is very tender, about 3 hours.
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Meanwhile, slit chiles lengthwise, then stem, seed, and devein. Tear chiles into roughly 1-inch pieces (you should have about 1 1/2 cups). Heat a comal or large heavy skillet (not nonstick) over medium heat until hot, then toast chiles, stirring constantly, until more pliable and slightly changed in color, 1 to 2 minutes. Transfer to a bowl. (Chiles will crisp as they cool.)
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Cover tomatillos with water in a medium saucepan and simmer, uncovered, until tender, about 10 minutes. Drain well, then purée with chiles, garlic, cilantro, and 1 1/2 tsp salt in a blender (in batches if necessary) until chiles are ground to small flecks.
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Transfer short ribs to a cutting board to cool. Strain meat juices remaining in pot into a glass measuring cup. Let fat rise to top and skim off. Coarsely chop or shred meat, discarding bones.
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Heat oil in a heavy medium pot over medium-high heat until it shimmers, then cook one fourth of tomatillo sauce (it will spatter), stirring, until slightly thickened, about 2 minutes. Add remaining sauce and meat juices and simmer, stirring occasionally, 10 minutes. Add meat. Thin sauce with water if necessary. Simmer, stirring occasionally, until heated through, about 4 minutes.