Cut a circle, at an inward angle, around pepper stems. Remove tops; scoop out seeds and membranes, like a tiny pumpkin.

Cut mozzarella into thumbnail-sized cubes, varying sizes slightly to fit each pepper. Cut prosciutto slices in half; wrap around mozzarella cubes. Stuff into pepper openings.

Add olive oil to a jar or lidded container. Whisk in Parmesan cheese, garlic, oregano, thyme, salt, black pepper, and pepper flakes to combine.