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 sterilized jar or lidded container. Whisk in Parmesan cheese, garlic, oregano, thyme, salt, black pepper, and pepper flakes to combine.
Add peppers to oil mixture; seal the jar. Marinate 5 to 6 hours. Serve straight out of the jar.
