Quesabirria Tacos

Name: Quesabirria Tacos
Ingredients: 2 tablespoons beef base, such as Better than Bouillon; 4 ancho chiles, seeds and stems removed; 4 guajillo chiles, seeds and stems removed; 4 cloves garlic; 1 Roma tomato, chopped; 2 white onions, 1 quartered and 1 diced; 1 tablespoon avocado oil; 4 pounds chuck roast, cut into large (2- to 3-inch) chunks; 2 pounds bone-in, English-cut short ribs; Kosher salt and freshly ground black pepper; 2 teaspoons Mexican oregano; 1 teaspoon ground cumin; 1 bay leaf; 16 to 20 yellow corn tortillas, warmed so they are pliable; 4 to 5 cups shredded Chihuahua or Oaxaca cheese; 1/4 cup chopped cilantro; Lime wedges, for serving