Rinse the olives in water twice, then dry them very well. Put them in a medium bowl and toss with the EVOO.
Fill a countertop fryer with oil or pour a few inches of oil into a large Dutch oven. Heat the oil to 350 degrees . (If using a Dutch oven, use a deep-fry thermometer to check the temperature.)
Set up a breading station: Line up 3 shallow bowls on the counter. Spread the flour out in one, beat the eggs in the second, and mix the breadcrumbs, pecorino, parsley and thyme in the third.
Using a chopstick, stuff the olives with the sausage. Coat the olives in the flour, then in the egg, then in the breadcrumb mixture, pressing to adhere.
Working in batches, fry the olives until deep golden, stirring occasionally, about 3 minutes per batch. Drain.