Re-season potatoes with salt and pepper, stir in cheese. Take a mayonnaise or peanut butter lid, line with plastic wrap to use as a mold. Pack the potato mixture into the lid, unwrap it and place the patty on a baking sheet. You may refrigerate them covered with plastic wrap until the next day, or fry immediately.
To cook, dredge the patties in flour. Heat olive oil in a skillet over medium-high heat, add patties. Just before frying, dredge the patties again with flour.
Add the patties to the oil without crowding them (you may have to cook them in batches). Cook until underside is golden brown, about 5 minutes, flip and brown the other side. Remove from the skillet and drain on paper towels. Serve hot with leftover gravy.