Remove seeds from 2 dried ancho or pasilla chiles; toast in a dry small skillet over medium-high heat, turning, until darkened and fragrant, about 4 minutes. Place in a medium bowl. Add 2 cups hot water; let sit until softened, about 5 minutes. Pulse chiles in a food processor with 1/2 cup soaking liquid, 1 garlic clove, and 2 tablespoons tomato paste until smooth. Heat 2 tablespoons olive oil in a large pot over medium heat. Cook 1 thinly sliced medium onion, stirring occasionally, until translucent, 68 minutes. Add 2 tablespoons chile paste and cook, stirring, until thick and darkened, about 4 minutes. Add two 15-ounce cans white hominy, rinsed, 8 cups turkey stock or low-sodium chicken broth, and 2 cups shredded cooked turkey meat; season with salt and pepper. Simmer until flavors meld, 1015 minutes. Serve with tortilla chips, sliced avocado, cilantro sprigs, and lime wedges.