Combine first four ingredients.
Preheat a pan or grill pan on medium heat.
Brush each side of a tortilla with olive oil. Sprinkle 1/4 cup Peperoncino cheese on one half of tortilla. Top cheese with a quarter of the peach mixture. Top with 1/4 cup cheese and fold over to close. Repeat with remaining tortillas.
Add quesadillas to pan and cook for 3 minutes per side until the cheese is melted and the tortilla is crisp.
Slice each quesadilla into thirds. Serve immediately.