Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add ground beef and cook, breaking it up with a spoon, until browned and cooked through, about 5-7 minutes.
Add diced onion and minced garlic to the beef and cook until the onion is softened, about 3 minutes.
Stir in the rice, black beans, diced tomatoes with green chilies (including liquid), beef broth, chili powder, cumin, smoked paprika, oregano, salt, and black pepper.
Bring the mixture to a boil, then reduce heat to low and cover with a lid.
Simmer for 18-20 minutes, or until the rice is tender and the liquid is absorbed.
Remove from heat and sprinkle shredded cheddar cheese over the top. Cover again and let sit for 3-5 minutes until the cheese melts.
Warm the flour tortillas in a dry skillet or microwave until pliable.
To serve, spoon the beef and rice mixture onto each tortilla, sprinkle with chopped cilantro, and roll up burrito-style.