Soak the dried guajillo and ancho chillies in hot water for 10 minutes until softened.
In a blender, combine the softened chillies, garlic, onion, bay leaves, oregano, cumin, paprika, salt, and pepper. Blend until smooth.
Coat the beef with the marinade, cover, and refrigerate for at least 4 hours or overnight.
In a Dutch oven or slow cooker, add the marinated beef and enough water or broth to cover it. Slow-cook on low for 3–4 hours until the meat is tender and shreddable.
Make the Consommé Sauce:
Remove the cooked beef from the pot and shred it.
Strain the cooking liquid to remove solids, creating a rich consommé sauce for dipping.
Assemble the Pizza:
Preheat your oven to 450°F (230°C).
Roll out the pizza dough on a floured surface to your desired size and thickness.
Spread a thin layer of consommé sauce over the dough instead of traditional pizza sauce.
Top with shredded birria beef and mozzarella or Oaxaca cheese.
Bake the Pizza:
Place the pizza on a baking sheet or pizza stone and bake for 12–15 minutes until the crust is golden and the cheese is bubbly.
Serve:
Slice the pizza and serve it with a side of warm consommé for dipping.
Garnish with fresh cilantro, diced onions, lime wedges, and jalapeños if desired.