Butter one side of each slice of sourdough bread.
Place four slices, buttered side down, on a clean work surface.
Sprinkle each slice with mozzarella and Monterey Jack cheese.
Evenly divide the shredded birria beef over the cheese.
Sprinkle with chopped cilantro, if using.
Top with another layer of cheese.
Cover with the remaining bread slices, buttered side facing outward.
Heat a large skillet or griddle over medium heat.
Cook each sandwich for 3–5 minutes per side, or until golden brown and the cheese is fully melted.
Slice in half and serve immediately with warm birria consommé for dipping, plus lime wedges, onion, and cilantro if desired.