Preheat oven to 375°F. Wrap tortillas in foil and keep in oven for 10 minutes.
Heat oil in a large saucepan over medium heat. Add onion and cook until soft and translucent, about 4 minutes. Increase heat to medium-high, add ground beef and cook, stirring occasionally, until thoroughly browned, about 5 minutes. Stir in chili powder; season with salt and pepper to taste. Transfer beef to colander to drain.
Pour 1 jar of enchilada sauce into a 9-by-13-inch baking dish. Spoon about 1/3 cup ground beef and 5 Tbsp. mixed cheeses inside each warm tortilla, roll up in cigar fashion and place enchiladas seam side down next to each other in baking dish. Cover evenly with second jar of enchilada sauce and remaining cheese. Bake in 375°F oven until bubbling, about 15 minutes.