Brush one side of each tortilla with the oil. Turn the tortillas over and top with the Monterey Jack, onion, corn, jalapenos, and cilantro. Sandwich with the remaining tortillas, oiled-side up.
Working in batches, if necessary, transfer the quesadillas to a foil-lined toaster-oven tray. Bake, turning once, until the cheese melts, 6 to 8 minutes total. Serve with the sour cream and salsa (if using).
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