Heat oven to 375°F (190°C) and lightly oil a 9-by-13-inch baking dish.
Cook onion in oil until soft, about 4 minutes. Add garlic and spices and stir for 30 seconds.
Add ground beef and cook, breaking it up, until no pink remains and the thickest pieces reach 160°F (71°C). Drain excess fat and season.
Spread a thin layer of enchilada sauce in the dish. Warm tortillas until pliable, fill each with beef and a little cheese, roll, and arrange seam-side down.
Pour remaining sauce over the tortillas, top with remaining cheese, and bake 20–25 minutes until bubbling. Rest 5 minutes before serving.