Authentic Quesabirria Recipe Tijuana, Mexico

Name: Quesabirria (Birria tacos)
Prep time: 45 min
Cook time: 4 h
Yield: 10 servings
Cuisine: Mexican
Ingredients: 5 qt (5 L) water, divided, plus more if needed; vegetable oil, for sautéing; 2.2 lb (1 kg) tomatoes, halved; 1 large onion, quartered; 12 garlic cloves; 1 tbsp dried thyme; 1 tbsp whole cumin seeds; 1 tbsp dried oregano; 2 tbsp black peppercorns; 1 tbsp allspice; 2 tbsp salt, plus more when needed; 10-12 bay leaves; 3 pasilla or chile negro peppers, stems and seeds removed; 12 guajillo or mirasol chile peppers, stems and seeds removed; 3 mulato or ancho or pasilla chile peppers, stems and seeds removed; 1 cinnamon stick, crushed; 1 oz (30 ml) apple cider vinegar; 3.3 lb (1.5 kg) beef shanks; 3.3 lb (1.5 kg) beef short ribs; SALSA; 6 tomatillo tomatoes, halved; 8 hile cambray or chile de árbol; 1/2 garlic clove; salt, to taste; FOR ASSEMBLING; corn tortillas; Oaxaca, Manchego, or Asadero cheese; cilantro, finely chopped; onions, finely diced; limes wedges, for squeezing over