Brown beef and onion in a large skillet over medium-high heat 7 to 8 minutes, breaking into small crumbles, until beef reaches 160°F. Drain excess fat.
Stir in cumin, chili powder, salt, and water. Simmer 2 minutes until moist with no free liquid; transfer to a bowl.
Scatter half the cheese over half of each tortilla. Divide beef over cheese; add remaining cheese. Fold bare halves over.
Wipe skillet; brush with 1 teaspoon oil. Cook two quesadillas over medium heat 2 to 3 minutes per side until golden. Repeat with remaining oil and quesadillas.
Rest 1 minute before cutting into wedges. Divide salsa and sour cream among four servings.