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TO MAKE THE PORK: Preheat the oven to 325F.
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Combine the chili powder, cumin, coriander seed, the 1 tablespoon salt, and black pepper in a small bowl.
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Place the pork in a roasting pan and evenly rub the spice mixture all over the meat.
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Add enough water to the pan to cover the first inch of the meat, which will ensure the pork stays moist as it cooks.
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Cover the pan tightly with aluminum foil.
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Roast until the meat reaches an internal temperature of 190F on an instant-read thermometer, 5 to 6 hours.
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(When its done, stand back when first removing the foil to avoid a blast of heat and steam in your face.)
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The meat will be fork-tender and almost falling off the bone.
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Let the meat stand until it is cool enough to handle.
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Remove the bone and pull the meat apart into bite-size chunks.
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The meat can be stored in a covered bowl and refrigerated until ready to use.
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TO MAKE THE TOMATILLO SAUCE: Place the tomatillos, quartered onion, jalapenos, and garlic in a large saucepan, cover with water, and bring to a boil over medium-high heat; decrease the heat to medium-low, bring the vegetables to a low boil, and cook until the tomatillos are soft and their bright green color turns a dull yellow-green, about 7 minutes.
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When any of the tomatillos bursts and falls apart, the vegetables are done; remove from the heat immediately.
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Pour the tomatillo mixture into a colander set over a bowl or the sink to strain out the liquid.
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In the work bowl of a food processor fitted with the metal blade, puree the tomatillo mixture, lime juice, cilantro, and 2 teaspoons salt.
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Just before serving, peel, pit, and cut the avocado into coarse chunks, and puree with the tomatillo mixture until smooth in a food processor.
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TO ASSEMBLE AND SERVE THE QUESADILLAS: Pour the olive oil into a large skillet set over medium heat.
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Once the oil begins to shimmer, add the sliced onions and the poblano and Anaheim chiles and saute, shaking the vegetables occasionally, until they are soft and lightly caramelized, 10 to 15 minutes.
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Preheat an ungreased griddle or large skillet over medium heat.
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Have the shredded pork, tomatillo-avocado sauce, tortillas, caramelized vegetables, and shredded cheese within easy reach.
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Put as many tortillas on the griddle as will fit without touching.
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Spread about 1/4 cup shredded cheese on each tortilla, then cover half of them with about 3/4 cup of the shredded pork, a heaping spoonful of the caramelized vegetables, and 2 tablespoons tomatillo sauce each.
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Reserve the remaining sauce for dipping.
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Flip the cheese-only tortillas on top of the pork tortillas and cook, flipping if necessary, until the tortillas are crispy and browned on the bottom.
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Once grilled, using a long sharp knife or a pizza cutter, slice the quesadillas into quarters.
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Serve immediately on warmed platters with Ancho Dipping Salsa and remaining tomatillo sauce.
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Preheat the oven to 425F.
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Roast the tomatoes in the oven in a large baking pan for about 30 minutes.
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Remove from the oven; add the garlic, onion, and jalapenos, and drizzle with olive oil.
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Return the pan to the oven and roast for another 20 minutes.
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Meanwhile, place the ancho and chipotle chiles in a bowl and cover with boiling water.
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Use a plate or small bowl to weigh down the chiles, keeping them submerged.
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Soak them until softened, about 15 minutes.
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Drain the chiles.
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Set aside.
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When the roasted vegetables are done, remove the skins from the tomatoes and discard.
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In the work bowl of a food processor fitted with the metal blade, pulse the roasted vegetables in 2 separate batches.
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Dont over-pulse or youll end up with a pureed salsa, not a chunky one.
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Pour the processed salsa into a large bowl.
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Puree 2 of the reconstituted ancho chiles in the (unwashed) food processor.
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Stir the pureed chiles into the salsa mixture.
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Pulse the remaining anchos and the chipotles until finely chopped, but not pureed.
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Stir the chopped chiles, salt, sugar, and lime juice into the salsa.
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Cover and refrigerate until ready to use.
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The pork can be roasted up to 2 days in advance, covered and refrigerated until ready to use.
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If you really want to get a jump on things, the pork can be frozen for up to 3 weeks.
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Make sure it is double-wrapped in plastic wrap, then foil, to keep it from drying out.
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The tomatillo sauce can be made up to 4 days in advance, covered, and refrigerated, with the exception of the avocado, which should be added the day you plan to serve the dish.
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The caramelized onions and chiles can be made up to 1 day in advance, covered and refrigerated.
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The refrigerated ancho salsa will keep for up to 5 days.
