In a medium bowl, combine the turkey, stuffing, Parmesan and mashed potatoes. Scoop out ½ cup-sized balls of the mixture and form a well with your fingers. Fill with 2 teaspoons of cranberry sauce and seal in the center, shaping with your hands back into a ball. Place on a parchment-lined baking sheet and refrigerate for 30 minutes.
Meanwhile, place the flour, eggs and bread crumbs in separate bowls lined up next to each other. Heat 2 inches of vegetable oil in a 6-quart Dutch oven to 350° and line a plate with paper towels.
Dredge each chilled ball in flour, followed by egg and bread crumbs, until they are all breaded. Working in batches, fry the balls, turning as needed, until golden brown and warmed through, 3 to 4 minutes per batch. Transfer to the prepared plate to drain, then transfer to a platter and serve with gravy for dipping.