Place dried chile pieces in a bowl and pour boiling chicken broth over. Allow to soak for 30 minutes, keeping the chiles submerged with a small bowl or some other weight.
Meanwhile, preheat oven to 450 degrees and line a baking tray with aluminum foil. Place tomatoes and onion on tray and roast until blackened, 25 minutes for the tomatoes and 40 for the onion. Allow to cool briefly before removing skin from tomatoes and chopping everything into smaller chunks. Reduce oven to 350 degrees.
Transfer peppers and soaking liquid to a blender and puree on high for about a minute; add roasted tomatoes and onion, garlic, Balsamic and Wine Vinegars, coriander, cinnamon, cloves, salt, and pepper. Blend until a thick puree forms.
Heat 1 Tbs Olive Oil over medium heat in a large, deep-sided skillet. Cook puree, uncovered, about 5 minutes, stirring frequently. Remove from heat and set aside.
Meanwhile, heat remaining 3 Tbs Olive Oil over medium heat in a skillet large enough to comfortably hold all chicken pieces. (Or you can work in batches, but you'll want to cover the sauce to keep it warm.) Sautee chicken, turning once, until golden brown, about 6-7 minutes each side.
Arrange chicken in a single layer in a large casserole dish and pour sauce over, turning chicken pieces to coat and cover with the sauce. Cover the casserole and bake for 45 minutes. Uncover and bake another 15 minutes, basting once halfway through; the chicken should be fork-tender and just falling off the bone, and sauce should be bubbling. Serve immediately with cooked white rice and tortillas, passing plenty of sauce on the side.
* Dried guajillo and ancho chiles should be readily available in the "ethnic" section of most large supermarkets. They both tend to be sweetly fruity and relatively mild as far as chile peppers go, but be aware that individual spice tolerance varies greatly.
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