01 - Rinse the rice under cold water. In a saucepan, combine rice, water, and salt. Bring to a boil, reduce heat to low, cover, and simmer for 15 minutes. Remove from heat and let stand for 5 minutes. Fluff with a fork. Stir in lime juice and cilantro if using.
02 - In a large skillet, heat olive oil over medium heat. Add onion and cook until softened, about 3 minutes. Add garlic and cook for 30 seconds. Add ground beef and cook, breaking up with a spoon, until browned. Drain excess fat if needed. Stir in tomato paste, cumin, chili powder, smoked paprika, oregano, salt, and black pepper. Cook for 1 minute. Add beef broth or water and simmer for 5 minutes until slightly thickened.
03 - In a small saucepan over medium heat, combine black beans, cumin, chili powder, salt, and pepper. Heat for 5 minutes, stirring occasionally.
04 - Heat tortillas in a dry skillet or microwave until pliable.
05 - Lay a tortilla on a flat surface. Spoon a portion of rice, beef mixture, and beans down the center. Top with cheese, salsa, lettuce, tomato, and sour cream. Fold in sides and roll up tightly. Repeat with remaining tortillas.
06 - Serve burritos warm, with extra salsa and sour cream if desired.