Preheat oven to 350°F (175°C). Grease a 9x13-inch baking dish.
In a large skillet, cook ground beef over medium heat until browned. Drain excess grease. Add onion and garlic, and cook until softened, about 3-4 minutes.
Stir in taco seasoning mix and water. Simmer until the mixture thickens, about 5 minutes. Add refried beans and 1 cup of cheddar cheese. Stir until well combined and the cheese is melted.
Warm the flour tortillas slightly to make them pliable. Spoon an equal amount of the beef and bean mixture onto each tortilla. Roll up each tortilla, tucking in the sides, and place seam-side down in the prepared baking dish.
Mix the red and green enchilada sauces together in a bowl, then pour over the burritos in the baking dish. Sprinkle the remaining 1 cup of cheddar cheese over the top.
Bake in the preheated oven for 20-25 minutes, or until the cheese is melted and bubbly.
Garnish with chopped green onions and cilantro. Serve with sour cream and guacamole, if desired.