Step 1Place the olives in a bowl of cold water and let stand 30 minutes. Drain, add fresh cold water and let stand 30 minutes longer.
Step 2Place the soppressata in a small food processor and process almost to a paste. Transfer to a small bowl. Place the cheese in the processor, process almost to a paste and add it to the bowl with the soppressata, stirring to mix.
Step 3Drain the olives well. Pat completely dry with paper towels. Using your fingers or skewer, solidly pack the centers with about one-fourth teaspoon of the cheese-meat mixture. (A chopstick will help compact the filling.)
Step 4Place the flour in a wide shallow bowl and the panko in a second wide shallow bowl. Beat the eggs in a third shallow bowl.
Step 5Dredge each olive in the flour, shaking off the excess, then in the beaten egg, shaking off excess, and finally in the panko, pressing to coat as thickly as possible. Transfer each coated olive to a clean platter.
Step 6Pour the oil into a heavy skillet to a depth of about 3 inches. Heat until a few crumbs turn toasty brown when they hit the oil. Add the olives in batches and fry, turning as needed, until the crust is crisp and golden brown, about 1 to 2 minutes. Drain on paper towels. Cool slightly before serving. (Leftover olives are delicious the next day, crisped briefly in oil again before serving.)