Roast the fresh chiles: Place the poblanos and jalapenos on a rack set over a gas stove-top burner and heated over high heat. Roast until the skin on all sides of each pepper is charred, turning frequently, about 5 minutes. (If you have an electric or ceramic stove top, roast the chiles in the oven using the broiler setting until charred on all sides.) Wrap each pepper in plastic wrap and set aside until the peppers are cool enough to handle, then peel the skin (the skin should stick to the plastic wrap). Rub the plastic wrap against the skin to loosen and remove it; do not rinse the peppers to remove the skin, as rinsing will remove flavor. Stem and seed each pepper, then dice the peppers into one-fourth inch pieces.
In a large heavy-bottom pot (preferably earthenware or cast iron) heated over medium-high heat, toast the ground New Mexico chile powder, 2 tablespoons cumin, 1 tablespoon oregano and the coriander until fragrant, stirring constantly, 30 seconds to 1 minute.
Stir in the oil along with the diced onions. Cook, stirring frequently, until the onions are softened, about 5 minutes. Stir in the garlic and the achiote paste (be sure to mash the paste until thoroughly incorporated and there are no lumps). Stir in 1 can diced tomatoes (with liquid), and season with 2 teaspoons salt. Bring the mixture to a simmer, stirring to scrape any flavorings from the bottom of the pan.
Stir in the hominy and 4 cups broth, then stir in the diced poblanos and jalapenos. Bring the mixture to a gentle simmer and cook, uncovered, until the hominy is tender but still slightly chewy, about 30 minutes. Stir occasionally, adding broth if needed (the mixture will thicken as it simmers and the hominy cooks).
Stir in the paprika and celery salt, as well as the remaining cumin and oregano. Stir in the remaining diced tomatoes (with liquid) and vegetable broth, as well as the black, pinto and kidney beans. Taste and adjust the seasoning and flavorings as desired. Continue to gently simmer, uncovered, until the beans warm and the flavors marry, about 20 minutes.
Remove from heat, and thin if desired with additional broth. Taste and adjust the seasoning, acidity and heat with a little Tabasco, cider vinegar, or both. The chili is best made 1 day ahead to allow the flavors time to marry.
Achiote paste is available at Latin markets.
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