Brown beef and onion in a skillet over medium-high heat for 8 minutes until beef reaches 160°F. Drain excess fat and stir in garlic, cumin, ancho chile, salt and tomato paste for 1 minute.
Add water and simmer for 2 minutes until no loose liquid remains. Remove from the heat and stir in refried pintos and cheddar, then let cool for 10 minutes until warm but no longer steaming; cooling is included in prep time.
Warm tortillas in the microwave under a barely damp paper towel for 20 to 30 seconds until flexible. Divide filling below the center of each tortilla, fold both sides inward and roll tightly into closed packets, securing each seam with one wooden toothpick.
Heat frying oil in a deep heavy saucepan to 350°F, using a vessel large enough that the oil fills it no more than halfway. Lower 2 packets seam-side down into the oil and fry for about 3 minutes per side until golden and 165°F in the centers.
Drain on a rack and let the oil return to 350°F before frying the remaining 2 packets. Rest all chimichangas for 5 minutes, remove all 4 toothpicks and serve one per person with 1 tablespoon sour cream.