Heat olive oil in a large deep skillet or pot over medium-high heat.
Add the ground beef and cook, breaking it apart with a spoon, until browned and cooked through, about 5-7 minutes.
Add the diced onion and minced garlic to the beef and cook until the onion is translucent, about 3 minutes.
Stir in the rinsed rice, black beans, diced tomatoes with green chilies (including the liquid), and beef broth.
Add ground cumin, chili powder, smoked paprika, dried oregano, salt, and black pepper. Stir well to combine all ingredients.
Bring the mixture to a boil, then reduce heat to low and cover the pot with a tight-fitting lid.
Simmer for 18-20 minutes, or until the rice is tender and has absorbed most of the liquid. Avoid lifting the lid during cooking.
Remove the pot from heat and sprinkle shredded cheddar cheese evenly over the top. Cover again and let sit for 5 minutes until the cheese melts.
Warm the flour tortillas in a dry skillet or microwave.
To serve, spoon the beef and rice mixture onto each tortilla, garnish with chopped cilantro, and add sour cream and salsa as desired.
Roll up the tortillas to form burritos and enjoy immediately.