In a large skillet over medium-high heat, brown the ground beef until fully cooked, approximately 5-7 minutes. Drain excess rendered fat.
Add the diced onion and minced garlic to the beef; sauté for 3 minutes until the onions are translucent.
Incorporate the cumin, chili powder, salt, pepper, and refried beans into the beef mixture. Stir continuously until the filling is uniform and heated through.
Lay each flour tortilla flat. Place approximately 1/2 cup of the beef and bean mixture and 1/3 cup of shredded cheese in the center of the tortilla.
Fold the left and right sides of the tortilla over the filling, then roll tightly from the bottom to the top to form a sealed cylinder.
Heat the vegetable oil in a heavy-bottomed pot or deep fryer to a temperature of 375°F (190°C).
Carefully place the prepared chimichangas into the hot oil, seam-side down, to seal the tortilla. Fry for 2-3 minutes per side until the exterior is golden brown and crispy.
Remove with a slotted spoon and place on a wire rack or paper towels to drain excess oil before serving.