Heat the olive oil in a large skillet over medium heat. Add the diced onion and sauté until translucent, about 3-4 minutes. Add the minced garlic and cook for an additional minute.
Stir in the black beans, cooked rice, ground cumin, and chili powder. Season with salt and pepper to taste. Cook the mixture for about 5-6 minutes, until heated through and well combined.
Remove the skillet from heat and stir in half of the shredded cheese, allowing it to melt slightly into the mixture.
Warm the flour tortillas in a tortilla warmer or foil in a low oven (or microwave for a few seconds) until pliable.
To assemble each burrito, lay a warm tortilla on a flat surface. Spoon about a quarter of the bean and rice mixture onto the center of the tortilla. Top with additional shredded cheese (to taste) and any optional toppings you desire.
Fold in the sides of the tortilla, then roll it from the bottom to the top to enclose the filling. Repeat with the remaining tortillas and filling.
Optional: Place the filled burritos seam-side down in the skillet used for filling, medium-side heat, until golden brown and crispy on both sides, about 2-3 minutes per side.
Serve warm with your choice of salsa, avocado, sour cream, or cilantro.