In a large bowl, combine the mashed potatoes, cheese, eggs, flour, green onion, salt and pepper. If the mixture appears runny or doesn't hold shape, add in a bit more flour until it does.
Use a muffin scoop or spoon to scoop about ¼ cup of potatoes onto a parchment lined plate or baking dish. Flatten the potato cakes until they are about half an inch thick. Place in freezer for 5-10 minutes to firm up.
Heat the oil in a large skillet over medium high heat or until the temperature reaches 325 degrees. Add the mashed potato cakes to the skillet, being careful not to crowd, and fry for about 3-4 minutes per side. You want the potato cakes to be a golden brown in color. Remove from heat and place on paper towels to drain. Repeat with remaining cakes.
Serve warm with a bit of sour cream. These are best eaten immediately.
Notes
Mashed potatoes are all going to have a different consistency. You will need to adjust the amount of flour used in this recipe so that the cake holds together. I find that half a cup of flour is usually sufficient.
If your mashed potato cake is hard to form, chill it in the freezer for a couple of minutes to firm up before frying.
You don't need a lot of oil for this recipe. It is a shallow pan fry and you should use just enough to coat the bottom of the pan.
Be careful not to crowd the cakes as you frying them. Work in batch of 3-4 cakes at a time.
Drain the cakes on paper towels after frying and sprinkle with a bit of kosher salt.
These are great served warm, as an appetizer or snack, with a dollop of sour cream on top.