Heat about 11/2 inches oil to 360°F in a 3 1/2-to 4-quart heavy saucepan.
Meanwhile, double-coat bocconcini by dipping in eggs, then in bread crumbs, and repeating. Transfer to a sheet of wax paper.
Working in batches of 10, lower balls into oil with a slotted spoon and fry, turning occasionally, until golden brown, about 30 seconds per batch. Transfer to paper towels to drain and season with salt. (Return oil to 360°F between batches.)