Add enough oil to fill a large, heavy Dutch oven a third of the way and heat to 180°C. Add the sausage, Parmesan, 1 tablespoon parsley and the red pepper flakes to a bowl and mix well. Add to a piping bag with a plain tip. Drain the olives and dry them very well with paper towels or a clean tea towel.
Pipe the sausage filling into each olive. Add the flour to a casserole dish and season with salt and pepper. In a second casserole dish, beat the eggs. In a third casserole dish, add the breadcrumbs, the remaining 1 tablespoon parsley, season with salt and pepper and whisk together.
Dredge each stuffed olive first through the flour, shaking to remove any excess, then through the egg and then into the breadcrumbs. Pack the breadcrumbs around each olive if necessary. Add to a clean plate. You can refrigerate them now if you are prepping for a party. Fry the olives, in batches, until golden and crisp and the pork is cooked through, 1 to 2 minutes. Remove to a paper towel-lined plate.