Heat 1 tablespoon olive oil in a pan over medium-high heat. Add onion and garlic; saute for 5 to 7 minutes. Add beef, cumin, salt, and pepper; cook and stir until beef is browned and crumbly, 5 to 7 minutes. Drain and discard grease.

Pour beef mixture into a large bowl and add sour cream and Monterey Jack cheese. Mix well.

Lay out wonton wrappers and add 1 teaspoon of filling to each. Wet your fingertips and seal wraps, folding ends diagonally and folding and pinching corners.

Heat 1/2 inch of oil in a frying pan over medium heat. Deep-fry wontons in the hot oil, 2 to 3 minutes each. Drain on paper towels.