In a saucepan over medium heat, add the vegetable oil. Once heated, stir in the flour and cook for a couple of minutes until it forms a smooth paste. Add the chili powder, ground cumin, garlic, and dried oregano. Stir well to combine the spices with the flour mixture. Gradually pour in the beef broth and tomato sauce, stirring constantly to avoid lumps.
Bring the sauce to a simmer and let it cook for about 10 minutes until it thickens to your desired consistency. Season with salt and pepper to taste. Set the sauce aside.
Take a large flour tortilla and place it on a clean surface. Spread a layer of refried beans in the center of the tortilla. Add your cooked protein of choice on top of the beans, followed by shredded cheese
Fold the sides of the tortilla inward, then roll it tightly to form a burrito. Repeat this process for the remaining tortillas and filling.
Preheat your oven to 350F. Take a baking dish and spread a small amount of the sauce on the bottom. Place each assembled burrito in the dish, seam side down. Pour the remaining sauce generously over the burritos until they are completely covered.
Cover the baking dish with aluminum foil and place it in the preheated oven. Bake for about 20 minutes, or until the burritos are heated through and the cheese is melted. Once cooked, remove the dish from the oven. Carefully transfer the wet burritos to serving plates using a spatula. Spoon some additional sauce from the baking dish over each burrito for extra moisture and flavor. Garnish with fresh cilantro, if desired.