Preheat the oven to 375°. In a medium bowl, combine 1-1/2 cups cheddar with the monterey jack and set aside.
Brush a rimmed baking sheet with 1 tablespoon olive oil. Arrange 6 tortillas on the sheet so that the surface is covered, overlapping as needed. Sprinkle the remaining 1-1/2 cups cheddar cheese evenly over the tortillas, leaving a 1/2-inch border on all sides; cover with the remaining 6 tortillas, overlapping as needed. Prick the top layer with a fork and bake until the tortillas begin to brown, about 10 minutes.
In a large skillet, heat the remaining 2 tablespoons olive oil over medium heat. Add the onion and cook until golden-brown, about 10 minutes. Add the beans and 1/4 cup water and mash until the beans are soft and the liquid is absorbed, about 5 minutes. Season with salt and pepper.
Spread the bean mixture over the tortillas, leaving a 1/2-inch border. Top with the taco sauce, chiles, chorizo and reserved cheese mixture. Bake until the cheese is melted, 25 to 30 minutes.