When I was a kid, any time we had leftover mashed potatoes, my mom would make potato pancakes out of them. I was grown before I knew you could make them any other way. Mama's potato pancakes were ok, but just not my favorite thing. Later, I learned how to make them where they were a lot better and I didn't have to have leftover mashed potatoes to do it.
about 4 cups grated raw potatoes (I used the packaged hashbrowns in the dairy section of the store)
1 small onion, peeled and finely chopped (or a bunch of green onions, cleaned and chopped)
1/2 cup flour (gluten free works well too)
1/2 tsp. baking powder
seasoning to taste (I use Mrs. Dash)
1/2 cup grated cheese, Parmesan is what I usually use, but a sharp cheddar works too
Mix all together well and heat a non-stick skillet with a couple tablespoons each of butter and olive oil. Scoop up enough of the potato mixture about the size of a golf ball, flatten slightly and place in the heated butter/oil mixture. Cook until brown on one side, turn, flatten with the spatula and brown on the other side. Eat while hot.
To turn them into a main course, add some chopped ham to the potato mixture. For a change of taste, add some crisp crumbled bacon to the mixture and try in a bit of the bacon fat. Not health food, but quite tasty.