Heat vegetable oil in a large skillet over medium-high heat.
Add diced potatoes in a single layer, season with salt, pepper, and paprika or taco seasoning if using.
Cook potatoes for 10 to 15 minutes, stirring occasionally, until golden and crispy, then set aside.
In the same skillet, cook ground beef over medium heat until browned; drain excess fat.
Stir in chili powder, cumin, garlic powder, onion powder, salt, black pepper, smoked paprika (if using), and water or beef broth.
Simmer the beef mixture for 3 to 5 minutes until slightly saucy.
Warm the flour tortillas slightly.
Assemble each burrito by layering potatoes, seasoned beef, and a generous amount of shredded cheese on the tortilla.
Add optional toppings such as sour cream, salsa, hot sauce, green onions, or jalapeños if desired.
Fold in sides and roll up the burrito tightly.
Optionally, toast the burritos in a skillet over medium heat for 2 to 3 minutes per side until golden and crisp.