Preheat the oven: Begin by preheating your oven to 375°F. Grease a 9x13-inch baking dish with non-stick spray or a small amount of butter.
Prepare the cheese: In a mixing bowl, combine 8 oz Monterey Jack cheese and 8 oz cheddar cheese. Mix well to ensure the cheeses are evenly distributed.
Make the sauce: In a medium saucepan, melt ¼ cup unsalted butter over medium heat. Once melted, sprinkle in ⅓ cup flour and whisk to form a roux. Cook for about 1 minute until it turns a light golden color.
Gradually add 2½ cups beef broth to the roux, whisking continuously to avoid lumps. Add 1 tablespoon chili powder, 1 teaspoon cumin, 1 teaspoon salt, ½ teaspoon pepper, and ½ teaspoon paprika. Let the mixture simmer, stirring occasionally, until it thickens (about 5-7 minutes).
Ladle some sauce: Pour a small amount of the sauce into the bottom of the greased baking dish, spreading it evenly.
Warm the tortillas: To make them easier to roll, warm the 12 corn tortillas in the microwave for 30-45 seconds until they are soft and pliable.
Fill and roll: Take a tortilla, spoon in a generous portion of the cheese mixture, and roll it up tightly. Place the rolled enchilada seam-side down in the prepared baking dish. Repeat for all tortillas.
Top with sauce: Once all the enchiladas are in the baking dish, pour the remaining sauce over the top. Sprinkle the leftover cheese mix on top of the sauce.
Bake: Cover the dish with aluminum foil and bake in the preheated oven for 20 minutes. After 20 minutes, remove the foil and continue baking for an additional 5 minutes until the cheese is bubbly and golden.
Cool and serve: Allow the enchiladas to cool for 10 minutes before serving. This will help the sauce thicken slightly and make them easier to serve.