Heat a large skillet over medium heat. Add the ground beef and chopped onion. Cook until the beef is browned and the onions are soft—about 7–8 minutes. Drain excess fat carefully.
Reduce heat to low and stir in cumin, chili powder, garlic powder, salt, and pepper. Once spices are evenly mixed, remove from heat and immediately stir in the cheddar and mozzarella cheeses. The residual heat will melt the cheese into the meat mixture.
Lay out each tortilla on a clean surface. Spoon about ¼ cup of the beef and cheese mixture into the center. Fold in the sides, then roll up tightly like a burrito, tucking in the ends to keep the filling secure.
In a large frying pan, heat 2 cups of vegetable oil over medium-high heat (about 350°F). Carefully place the chimichangas seam-side down into the hot oil, cooking 2–3 at a time. Fry for 2–3 minutes on each side, until golden brown and crispy. Use tongs to turn them gently.
Remove chimichangas and set them on a plate lined with paper towels to drain any excess oil. Serve hot with sour cream, salsa, or guacamole.