Preheat oven to 350°F (175°C). In a large skillet over medium-high heat, add the ground beef and break it apart with a wooden spoon. Cook for 5–7 minutes until fully browned, then drain any excess fat. Stir in the taco seasoning along with the amount of water specified on the seasoning packet and cook until thickened.

In a medium saucepan, melt the butter over medium heat. Once melted, stir in the flour and cook for 1 minute to remove the raw flour taste. Slowly whisk in the beef broth, ensuring there are no lumps, then add the enchilada sauce and chili powder. Bring to a gentle simmer and cook until slightly thickened, about 5 minutes.

Lay out the tortillas on a clean surface. Spread a generous spoonful of refried beans down the center of each tortilla, followed by a scoop of rice, some of the cooked beef mixture, and about 1½ cups of the shredded cheddar cheese (divided evenly among the burritos). Fold in the sides of each tortilla, then roll tightly to form a burrito.

Spray a 13×9-inch baking dish with non-stick spray. Place the burritos seam-side down in the dish. Pour the sauce evenly over the top, making sure each burrito is well covered. Sprinkle the remaining cheese over the sauce.

Place the baking dish in the preheated oven and bake for 20 minutes, or until the cheese is fully melted and the burritos are heated through.

Remove from the oven and let cool slightly before serving. Garnish with sour cream, shredded lettuce, diced tomatoes, and fresh cilantro if desired. Serve immediately with tortilla chips and salsa on the side.