Remove stems and seeds from guajillo and ancho chiles. Toast in a dry skillet over medium heat for 30 seconds per side until fragrant. Soak in hot water for 15-20 minutes until soft, then drain.
Add rehydrated chiles to a blender with chipotle pepper, adobo sauce, diced tomatoes, onion, garlic, cumin, oregano, cinnamon, cloves, vinegar, and 1 cup of beef broth. Blend until smooth and season with salt and pepper.
Pat beef chunks dry, season generously with salt and pepper. Sear in hot oil over medium-high heat for 2-3 minutes per side until deeply browned. Transfer to slow cooker.
Pour chile sauce over seared beef in the slow cooker. Add remaining beef broth and bay leaves. Cook on LOW for 8 hours or HIGH for 4-5 hours until beef is fall-apart tender. Remove and discard bay leaves.
Remove beef and shred into bite-sized pieces. Strain braising liquid through a fine mesh strainer into a small saucepan. Simmer for 10-15 minutes until slightly thickened to a thin tomato sauce consistency. Season to taste.
Place pizza stone or baking sheet on lowest oven rack. Preheat to 500°F (260°C) for at least 30 minutes. Dust baking sheet with cornmeal or brush with oil if not using a stone.
Let pizza dough rest at room temperature for 20-30 minutes. On a floured surface, stretch or roll dough to a 12-inch diameter with a slightly thicker edge for the crust.
Transfer shaped dough to parchment or oiled baking sheet. Brush lightly with olive oil. Par-bake for 5-6 minutes until surface looks matte and crust is just set but not fully cooked.
Spoon 1/2 cup reduced consomé over par-baked crust in a thin, even layer. Top with shredded Oaxaca cheese, mozzarella, shredded birria beef, and sliced jalapeños.
Return pizza to oven and bake for 8-10 minutes until cheese is melted and bubbly, edges are golden and crispy. Broil for 1-2 minutes for extra browning if desired. Let rest 2-3 minutes before slicing.
Top with fresh diced white onion and chopped cilantro. Serve with lime wedges and small bowls of warm consomé for dipping.