Put the chilies in a heatproof bowl and add boiling water to cover. Let stand to soften while you cook the chicken and char the vegetables.

In a large saucepan, combine the chicken, oregano, ½ teaspoon of the cumin, 1 teaspoon salt, ½ teaspoon pepper and 6 cups water. Bring to a simmer over medium-high, then reduce to medium-low and simmer, uncovered, until a skewer inserted into the chicken meets just a little resistance, about 15 minutes. Transfer the chicken to a large plate; set aside. Remove the pan from the heat; cover to keep the broth warm.

While the chicken cooks, heat a large Dutch oven over medium-high until water flicked onto the surface immediately sizzles and evaporates. Put the tomatillos, tomato, onion and garlic in the pot; cook, turning occasionally, until charred and softened, 10 to 15 minutes. Transfer to a blender jar as they are done. When all have been charred, set the pot aside.

Drain the chilies and add them to the blender with the vegetables, along with ½ teaspoon salt. Blend on high until smooth, about 2 minutes, scraping the blender jar as needed.

In the same Dutch oven over medium, combine the oil, the remaining ½ teaspoon cumin and the cloves. Cook, stirring, until fragrant, about 1 minute. Carefully add the puree (it may splatter); reserve the blender jar. Cook, scraping up any browned bits, until thickened and deepened in color, about 10 minutes. Stir in 2 cups of the warm broth, bring to a simmer and cook, stirring, for 10 minutes. Meanwhile, add the tortillas to the now-empty blender along with 1 cup warm broth. Let stand for 5 minutes to soften, stirring after a couple minutes to ensure even soaking, then puree on high until smooth, about 1 minute.

Stir the tortilla puree into the sauce in the Dutch oven and return to a simmer. Add the chicken and any accumulated juices; cook, uncovered and occasionally turning the chicken, until a skewer meets no resistance and the sauce clings, about 15 minutes. Off heat, taste and season with salt and pepper. Serve with cilantro, lime wedges and warm tortillas.