Dip each croquette into beaten egg, then roll in bread crumbs. Set back on lined pan. Heat oil in a heavy bottomed skillet to 375 degrees. Line a sheet pan with paper towels.
Drop in about 5-6 at a time, turning often, and fry until crisp and golden brown. This will only take about a minute for each ham croquette, they continue to cook and darken slightly once removed.