To cook the chicken, place the bird in a large pot with a lid. Add water just to cover, add the garlic, the whole onion, the oregano, the bay leaves, the salt, and the pepper. Bring slowly to a simmer, uncovered, which may take as long as 30 minutes. Skim off any scum that appears.

Simmer the chicken gently for just 20 minutes. Cover the pot and remove from the heat. Let the chicken cool in the water for 2 hours. The meat will be tender and juicy.

Remove the chicken to a platter. Pour the stock through a fine-mesh sieve placed over a large bowl. Place briefly in the refrigerator to force the fat to rise, then spoon away the fat. Measure out 1 cup of the stock to use for the sauce; cover and refrigerate or freeze the remaining stock for future use.

When the chicken is cool enough to handle, remove and discard the skin, then remove the meat from the bones. Shred the meat into a big bowl. Add the thyme and grated onion and season with salt and pepper. Cover and set aside.

To make the sauce, preheat a broiler. Place the chiles on a baking sheet and slip under the broiler. Broil, turning as needed, until the skins blister and blacken on all sides. Wrap in a kitchen towel or drop into a plastic or paper bag until cool, then peel and seed. Set aside.

Meanwhile, bring a saucepan filled with salted water to a boil. Add the tomatillos and simmer until tender, about 10 minutes. Drain and immerse in a bowl of ice water to halt the cooking. Drain well again.

Working in batches, in a blender, combine the roasted chiles, tomatillos, tomatoes, onions, garlic, jalapeños, cilantro, and cloves. Pulse to chop finely. Add small amounts of the stock to get the blender going and to smooth out the sauce. Season with the salt and pepper.

Heat 2 tablespoons oil in a saucepan over high heat. Add the sauce, which will splash a little, and simmer, uncovered, until slightly thickened, about 15 minutes.

Preheat an oven to 350°F. Keep the sauce warm over very low heat. Ladle a thin layer of the sauce over the bottom of a 9-by-13-inch baking dish.

Pour about 4 tablespoons oil into a small sauté pan over medium-high heat. Using tongs, dip a tortilla into the hot oil to soften it for rolling, then immediately dip it into the warm sauce. Lay the tortilla on a work surface.

Place a few tablespoons chicken filling, plus a tbsp or so of cheese across the bottom third of the tortilla. Roll up cigar fashion as tightly as possible. Place in the prepared baking dish, seam side down. Repeat until all the chicken filling and tortillas are used up.

Pour the remaining sauce evenly over the enchiladas. Bake for 10 minutes.

Remove from the oven and top evenly with the remaining cheese and the 1 cup sour cream. Return to the oven and continue to bake until the cheese melts and the sauce is bubbly, about 5 minutes longer.

Remove from the oven and serve piping hot. SERVING SUGGESTION: Top with more sour cream, cilantro, avocado, and grated radish, as desired. Serve piping hot.