1 1/4 cups shredded Monterey Jack cheese (4 ounces)
Preheat oven to 400 degrees. In a large skillet, heat oil over medium-high. Add garlic and cayenne; season with salt and pepper. Add black beans and stir to combine. Cook until beans are warmed through, 2 minutes. Remove from heat.
Arrange 5 tortilla halves in a 2-quart baking dish. Top with half the bean mixture and 1/2 cup salsa, then sprinkle with one-third the cheese. Repeat with another layer of tortilla halves, bean mixture, salsa, and cheese. Top with remaining tortilla halves, salsa, and cheese. Cover with foil and bake until center is hot and cheese melts, 10 minutes. Uncover and bake until cheese is bubbling, 5 minutes.