In a large skillet over medium heat, add a splash of oil and sauté the finely chopped onion until it becomes translucent, about 3-4 minutes. Add the minced garlic and cook for an additional minute, stirring frequently to prevent burning.
Add the pound of ground beef to the skillet, breaking it apart with a spatula. Cook until the beef is browned and cooked through, approximately 5-7 minutes. Drain any excess fat if necessary.
Once the beef is browned, sprinkle in the taco seasoning and pour in the cup of water. Stir well to combine and let the mixture simmer for about 5 minutes until the sauce thickens slightly.
Stir in the drained black beans and cooked rice, mixing until everything is well incorporated. Allow the mixture to heat through for another 2-3 minutes.
Lay out the large flour tortillas on a clean surface. Spoon a generous amount of the beef mixture onto the center of each tortilla, then sprinkle on a handful of shredded cheese.
To roll the burrito, fold in the sides of the tortilla and then roll from the bottom up, ensuring the filling is secure. Repeat with the remaining tortillas and filling.
Place the rolled burritos on a serving plate. Top with salsa, a dollop of sour cream, sliced avocado, and a sprinkle of fresh cilantro. Serve with lime wedges on the side for an extra burst of flavor.