Step 1: Prepare the Birria

1. In a dry skillet over medium heat, toast the chilies for 1-2 minutes until fragrant, being careful not to burn them.
2. Place the toasted chilies in a bowl, cover with hot water, and let them soak for 10-15 minutes.
3. In a blender, combine the soaked chilies, garlic, onion, tomato, apple cider vinegar, cumin, paprika, and oregano. Blend until smooth.

Step 2: Cook the Birria

1. Heat a large pot or Dutch oven over medium-high heat. Add the beef chunks and sear on all sides until browned.
2. Pour the chili mixture over the beef, add the cinnamon stick, bay leaves, and beef broth. Season with salt and pepper.
3. Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 2-3 hours, or until the beef is tender and shreds easily.

Step 3: Prepare the Consommé

1. Strain the birria cooking liquid into a separate bowl to create the consommé. Adjust seasoning as needed.
2. Keep the consommé warm for serving as a dipping sauce.

Step 4: Assemble the Sandwiches

1. Butter one side of each bread slice. Place a slice of bread, butter-side down, in a hot skillet or griddle.
2. Sprinkle a mix of mozzarella and Monterey Jack cheese onto the bread, then add a layer of shredded birria beef.
3. Top with another slice of bread, butter-side up. Grill the sandwich for 2-3 minutes on each side, or until golden brown and the cheese is melted.

Step 5: Serve

1. Slice the sandwiches in half and serve immediately with a small bowl of consommé for dipping. Garnish with chopped cilantro and diced onions if desired.