Heat olive oil in a large skillet over medium heat.
Add diced potatoes to the skillet and cook for 8-10 minutes, stirring occasionally, until they begin to soften and turn golden brown.
Add chopped onion and minced garlic to the skillet with the potatoes. Cook for 3-4 minutes until the onion becomes translucent.
Push the potato mixture to one side of the skillet and add the ground beef to the other side.
Cook the ground beef, breaking it apart with a spatula, until browned and cooked through, about 6-8 minutes.
Mix the potatoes, onions, and beef together in the skillet.
Sprinkle cumin, chili powder, smoked paprika, salt, and black pepper over the beef and potato mixture. Stir well to evenly distribute the spices and cook for another 2 minutes to let the flavors meld.
Warm the flour tortillas in a dry skillet or microwave until pliable.
Divide the beef and potato filling evenly among the tortillas, placing it in the center of each.
Top each filling with 1/4 cup shredded cheddar cheese, 2 tablespoons plain Greek yogurt, and a sprinkle of chopped fresh cilantro.
Fold the sides of the tortilla over the filling and roll tightly to form a burrito.
Serve immediately while warm.