In a large skillet, heat the oil over medium-high heat. Swirl to coat the pan, then add the beef. With the back of a spoon, press it out into a 1/2-inch thickness (it will look like one large patty). Let sizzle in the pan for 3 to 4 minutes, until it starts to form a crust.
Sprinkle with the chili powder, oregano, cumin, salt, garlic powder, and smoked paprika. Scatter the onion over the top. With a sturdy wooden spoon or spatula, break the meat up into small pieces. Continue to cook, stirring occasionally, until the meat is cooked through, about 4 minutes more.
Stir in the beans and salsa. Cook, scraping up any stuck-on bits, until the liquid has mostly cooked off and the beans are warmed through, about 1 minute. Taste and adjust the seasoning as desired.
Assemble the burritos: place a tortilla on your work surface and sprinkle a scant 3 tablespoons of cheese down the center in a line. Top with one-sixth of the beef/bean mixture (about 2/3 cup). Add another scant 3 tablespoons cheese on top.
Fold the two opposite sides of the tortilla that are near the short ends of the filling up and in, towards the center. Lift one of the two remaining tortilla sides up and over the filling, rolling it to secure. Repeat with remaining tortillas.
When ready to eat, warm a nonstick skillet over medium heat. Once the skillet is hot, lay a burrito in the skillet, seam side down. Let brown on the first side for 1 to 2 minutes until golden, then flip and brown on the other side. Let cool a few minutes, then serve hot with any desired toppings.
Notes
TO STORE: Refrigerate wrapped beef burritos in an airtight container for up to 4 days.
TO REHEAT:Warm in a skillet or microwave until heated through.
TO FREEZE: Wrap burritos tightly after assembling (but before toasting) and freeze for up to 3 months. Thaw overnight and reheat before serving.