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Stir collectively sausage, cheeses, 1 egg (about 2 tablespoons crushed egg), and, if desired, crushed pink pepper in an enormous bowl until correctly blended.
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Stir collectively 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 correctly to combine.
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Decrease a lengthwise slit down the facet 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 through exterior of each olive, rolling to completely enclose olive and forming a spherical kind.
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Working in batches, roll olives in flour, dip in remaining crushed eggs, and roll in remaining 1 1/2 cups breadcrumbs.
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Pour oil to a depth of 4 inches in an enormous Dutch oven; heat over medium-high until a deep-fry thermometer reads 350°F. Working in batches, fry until breaded olives begin to drift and are golden brown, about 4 minutes per batch. Take away from oil with a slotted spoon, and drain briefly on a baking sheet lined with paper towels. Sprinkle with pecorino and Parmigiano, and serve scorching.
Make Ahead
Stuffed olives could also be prepared by the use of step 3 and refrigerated in a single day. Let come to room temperature sooner than frying.
Immediate Pairing
Good, juicy Barbera d’Asti.