We love the smoky combination of cascabel and guajillo chiles. Using two varieties of dried peppers creates a complex sauce with wonderful depth of flavor, so we recommend seeking them both out. Look for the best-quality corn tortillas you can find. They will have a better flavor and texture and will be easier to work with.
Bring 3 cups water, the chicken, guajillo, cascabel, cilantro stems, garlic, 1 tablespoon kosher salt, peppercorns and coriander seeds to a boil in a large saucepan over medium-high heat. Reduce to a simmer, cover and cook on low until the chicken is cooked through, 20 to 30 minutes.
Remove the chicken from the liquid to a plate (reserve the cooking liquid) and set aside until cool enough to handle. Remove the skin and separate the meat from the bones; discard the skin and bones. Shred the meat into small pieces and put into a medium bowl.
Let the hot cooking liquid cool for 5 minutes or so, then transfer it to a blender, filling no more than halfway. Remove the center cap from the lid and place it on the blender. Cover the lid with a folded kitchen towel to catch splatters, and pulse until smooth. Pour the sauce into a medium bowl and repeat with any remaining cooking liquid. Season with salt.
Pour 1/2 cup of the chile sauce over the shredded chicken. Stir to combine and season with salt if necessary.
Position a rack in the center of the oven and preheat to 425 degrees F.
Heat the oil in a medium skillet over medium-high heat until it bubbles immediately when the edge of a tortilla touches the surface. Working one at a time, fry the tortillas until just starting to brown and crisp, about 10 seconds per side (they should still be somewhat pliable). Drain on paper towels.
Dip both sides of each tortilla in the chile sauce just to coat and transfer to a rimmed baking sheet. Spread 1/2 cup of the chile sauce in a 6-inch strip down the center of a 13-by-9-inch baking dish.
Spoon 1/4 cup of the shredded chicken across the center of a tortilla. Fold one side over the filling, then roll up the tortilla. Place seam-side down in the prepared baking dish. Repeat with more sauce and remaining tortillas (the enchiladas should be nestled right up against each other in the pan). Top with any remaining sauce in your bowl or leftover on the baking sheet. Cover tightly with foil and bake until the sauce bubbles, 20 to 25 minutes. Remove the foil, top with the cheese and bake until the cheese melts but doesn't brown, 5 to 10 minutes. Let sit 10 minutes.
Top the enchiladas with crema, cilantro leaves and onions. Serve with lime wedges for squeezing over.
Dried guajillo chiles are commonly found in many national grocery stores. Casabel chiles may be harder to find. Look for them in international groceries or substitute chipotles instead.
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