Place mashed potatoes, cheese, egg, and 3 tbsp flour in a bowl and stir to combine.
Take a scoop of the potato mixture and form into patties.
Place the remaining 4 tbsp of flour on a plate.
Lightly coat the potato patties in the flour.
Heat a thin layer of the oil or butter in a large saute pan over medium heat.
Cook the potato cakes for 3 minutes on each side for a total of 6 minutes.
Serve as is or with accompaniments.
*After step 2, place patties on a baking sheet and place in freezer for 30 minutes then place par-frozen patties in a ziploc bag and freeze up to 4 months. When ready, defrost in fridge for 24 hours and follow steps 3-7.