Quesadilla: Preheat the oven to 450 degrees F. Place 8 tortillas on an ungreased baking sheet. Spread half the cheese, onion and black pepper on each and season to taste with salt and pepper. Stack to make 2 layer layers, cover with remaining tortilla and brush the tops with oil and sprinkle with some of the Parmesan cheese. Place on a lightly oiled baking sheet and bake for 5 to 7 minutes or until the tortillas are lightly golden brown and the cheese has melted. Cut into quarters, top each quarter with a slice of prosciutto and drizzle with the rosemary oil.
Make the rosemary oil: Combine the oil, rosemary, chives and salt and pepper in a food processor and process until smooth. Strain through a fine strainer and store in the refrigerator.