In a large pan with a lid, heat the oil over medium heat. Add the onion and cook until translucent, about 3 minutes.
Add the garlic and cook for another 1 minute.
Stir in the cumin and smoked paprika to coat the aromatics.
Add the black beans, water, and tomato paste. Mix well, cover, and let simmer over low heat for 5–7 minutes.
Turn off the heat and add the cooked rice, lime juice, and cilantro if using. Stir until fully combined. Season with salt and pepper to taste.
To soften the tortillas, stack them on a microwave-safe plate, cover with a damp paper towel, and microwave for 10 seconds. Flip the stack and microwave for another 10 seconds.
To assemble, lay out a tortilla and add 1 cup of the filling near one edge. Fold the edge over the filling, fold in the sides, and continue rolling into a burrito. Repeat with remaining tortillas.
To freeze, wrap each burrito individually in freezer paper or foil and freeze.
To reheat:-Microwave: Unwrap, wrap in a damp paper towel, and microwave for 2–3 minutes or until heated through.-Toaster oven: Heat at 375°F (190°C) for 20 minutes, or until warmed through.