Instructions

1. Make the chicken: To a large pot or Dutch oven, add the chicken, chicken neck, and enough water just to cover. Add the carrot, onion, and 3 unpeeled garlic cloves, bring to a simmer, and cook until the meat is cooked through and the broth is flavorful, about 40 minutes.
2. Strain, reserving both the broth and the chicken. Let the chicken rest until cool enough to handle. Shred the meat and set aside; discard the bones and skin. (You should have about 4 cups of meat.) Reserve 8 cups of broth.
3. Make the sauce: In a small, dry skillet over medium-high heat, add the cumin. Cook, stirring or shaking the pan occasionally, until fragrant, about 3 minutes. Remove, then finely grind. Set aside.
4. In a large pot over medium-high heat, melt the butter. Once hot, add the chopped onion and cook, stirring occasionally, until softened and barely colored, about 8 minutes. Stir in the chopped garlic and cook for 1 minute, then sprinkle the flour into the pan and stir to incorporate. Add the chopped chiles, season generously with salt and lightly with black pepper, then add the reserved cumin and oregano; stir well. Gradually whisk in 6 cups of the chicken broth, bring to a simmer, and cook until the sauce is slightly thickened, about 10 minutes. Taste and adjust the seasoning as needed. Set aside.
5. Make the enchiladas: Preheat the oven to 400°F. Ladle 1½ cups of the sauce into a 9-by-13-inch glass baking dish. In a small pot, heat the remaining 2 cups of chicken broth. So they can be rolled without breaking, dip the tortillas very briefly in the hot broth until softened slightly.
6. Fill the enchiladas: Working one at a time, distribute about 3 tablespoons of shredded chicken down the center of each tortilla. Roll the tortilla loosely into a cigar shape to cover the filling, then transfer, seam side down, to the prepared baking dish, nestling it in the sauce. Repeat with the remaining tortillas and chicken, then ladle the remaining sauce over the top to generously coat the tortillas. Sprinkle with the grated cheese, cover with aluminum foil, and bake until the enchiladas are heated through and the sauce is beginning to bubble, about 20 minutes. Remove the foil and bake until the top is browned and very bubbly, 15–20 minutes more.
7. Remove the enchiladas from the oven and sprinkle with the queso fresco, scallions, and cilantro. Divide among 6 plates and drizzle or dollop each portion generously with crema or sour cream. Garnish each with the lettuce, tomato, and radish, if using. Serve hot.