In a large bowl, stir together mashed potatoes, egg, and Parmesan. Season with salt and pepper and mix well to combine (mixture will look wet). In a large nonstick skillet, heat vegetable oil over medium-high.
In batches, drop heaping spoonfuls of potato mixture into skillet, pressing with a spatula to flatten slightly. Cook until golden brown on bottom, about 3 minutes. Gently flip and cook until golden brown on other side, 3 minutes. Repeat with remaining potato mixture and more oil.
Don't go go the bother of boiling the potatoes and the mashing! A far simpler and tastier way is:
1. Prick a few holes in 2 inch diameter potatoes, dampen them and wrap in a paper towel with some salt and pepper.
2 Microwave them for 2 to 3 minutes, depending on size.
Cool and place whole on cutting board.
4. Press down on top of each with a fry pan or skillet to make 1/2 inch pancakes.
5. Season with salt and pepper or as desired.
6. Heat an oiled cast iron skillet on the grill and sear them.
I like add baccon biy's ans serve with eggs over easy for breakfast.
Poached eggs are also good.
I often make these but add green onions and serve with sour cream.