In a large 7-quart pot, add the chuck roast, short ribs with bones, halved onion, garlic bulb (unpeeled but with top cut off), carrots, bay leaves, and dried guajillo chiles.

Pour in hot water to cover all ingredients, filling the pot almost to the top.

Stir in the chicken bouillon, Mexican oregano, ground cumin, and salt. Bring the mixture to a boil over high heat.

After boiling for 30 minutes, skim off the foam and impurities that rise to the top of the broth to ensure a clear and clean flavor.

Remove the softened guajillo peppers, onion, garlic cloves (squeezed out of the bulb), and carrots from the pot. Place them in a blender or food processor and blend until smooth, adding up to 1/4 cup of the hot broth to help blend smoothly.

If your blender is not high-powered, strain the blended pepper mixture to remove any tough skins for a silky broth. This step can be skipped if using a powerful blender.

Stir the blended pepper sauce back into the broth. Add chili powder to enhance the color and depth of flavor as desired.

Cover the pot and simmer gently for about 3 hours, or until the meat is tender and easily shreds. Stir occasionally about every 40 minutes and taste the broth near the end to adjust seasoning.

Skim the fat from the top of the broth and pour it into a small skillet or saucepan; this flavorful grease will be used later for frying the tacos.

Remove the meat pieces from the broth, discard bones, and serve chunks in bowls with broth ladled on top. Garnish with diced onion, fresh cilantro, and lime wedges.

Finely chop the cooked meat into small pieces. Heat a large skillet or griddle over medium heat.

Dip each corn tortilla into the reserved grease, then place on the heated skillet.

Add a generous amount of chopped meat and sprinkle with cheese. Fold the tortilla over and press down with a spatula.

Cook for 2-3 minutes until the bottom side is golden and crisp, then flip and cook the other side until crisp and the cheese is melted. Optionally, spoon more grease on the tortilla while frying for extra color and flavor.

Remove the cooked quesabirria tacos from the skillet and let cool briefly. Top with diced onion and fresh cilantro if desired.

Serve with a bowl of the broth for dipping the tacos, accompanied by lime wedges.