Heat the olive oil in a large skillet over medium heat.
Add the onion and cook for about 4 minutes until softened. Stir in the garlic and cook for 30 seconds.
Add the ground beef and cook until browned, breaking it apart as it cooks. Drain any excess grease.
Season the beef with chili powder, paprika, cumin, oregano, salt, and pepper. Stir well.
Mix in the cooked rice, diced tomatoes, and green chilies if using. Cook for 2 to 3 minutes until everything is heated through.
Remove from the heat and stir in the cilantro.
Warm the tortillas slightly to make them easier to roll.
Place an even amount of the beef and rice mixture in the center of each tortilla.
Sprinkle with the cheddar and Monterey Jack cheese.
Fold in the sides and roll tightly into burritos.
Heat a clean skillet over medium heat and lightly brush with butter or olive oil.
Toast the burritos seam-side down for 2 to 3 minutes, then flip and cook until both sides are golden and crispy.
Serve warm with your favorite toppings.