Process ham in a food processor until finely chopped. Transfer to a medium bowl. Switch blade to grating attachment and pulse potato through feeding tube of processor. Add shredded potato to ham. Toss with flour and seasonings. Stir in egg to coat. Heat a large skillet over medium heat. Add oil to 1/4 inch and allow to heat up (do not let oil smoke). Using your hands, form firmly packed 1/4-cup mounds of the potato mixture and drop into the oil. Cook in batches of two to four (as much as your skillet allows without crowding the pan) until browned, about three minutes per side. Drain on paper towels. Serve immediately or reheat in a single layer in a 400ºF oven for five minutes. Chef’s note: If you do not have a processor, you can finely chop the ham by hand. A standard box grater will work for shredding potatoes.
