Heat olive oil in a large skillet over medium-high heat.
Add the chopped onion and cook for 3-4 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned and no longer pink, about 6-8 minutes.
Stir in the ground cumin, chili powder, smoked paprika, black pepper, and salt. Cook for 1 minute to toast the spices.
Add the drained black beans and beef broth to the skillet. Stir to combine and simmer for 5 minutes until slightly thickened.
Warm the whole wheat tortillas in a dry skillet or microwave for 20 seconds to make them pliable.
To assemble each burrito, lay a tortilla flat and add 1/4 cup cooked brown rice in the center.
Spoon about 1/2 cup of the beef and bean mixture over the rice.
Sprinkle 1/4 cup shredded cheddar cheese on top of the beef mixture.
Add a tablespoon of diced tomato and a tablespoon of chopped cilantro.
Top with 2 tablespoons of plain Greek yogurt.
Fold the sides of the tortilla over the filling and roll tightly from the bottom up to enclose the filling.
Repeat with remaining tortillas and filling.
Serve immediately or wrap in foil to keep warm.