How to Make It
Stir together sausage, cheeses, 1 egg (about 2 tablespoons beaten egg), and, if desired, crushed red pepper in a large bowl until well combined.
Stir together milk and 1/2 cup breadcrumbs in a medium bowl. Let stand until breadcrumbs absorb milk, about 5 minutes. Add breadcrumb mixture to sausage mixture, and stir well to combine.
Cut a lengthwise slit down the side of each olive. Take a small pinch (about 1/2 teaspoon) sausage mixture, and stuff inside each olive. Press about 11/2 tablespoons sausage mixture all around outside of each olive, rolling to completely enclose olive and forming a round shape.
Working in batches, roll olives in flour, dip in remaining beaten eggs, and roll in remaining 1 1/2 cups breadcrumbs.
Pour oil to a depth of 4 inches in a large Dutch oven; heat over medium-high until a deep-fry thermometer reads 350°F. Working in batches, fry until breaded olives begin to float and are golden brown, about 4 minutes per batch. Remove from oil with a slotted spoon, and drain briefly on a baking sheet lined with paper towels. Sprinkle with pecorino and Parmigiano, and serve hot.