Add mashed potatoes, cheese, chives, green onion, egg, and 1/4 cup flour to a large bowl. Stir to combine. Note that you should not need to add salt and pepper if your mashed potatoes are seasoned well. If they are bland, season the mixture with salt and pepper to taste.

Add remaining 1/4 cup flour to a shallow plate or bowl. Season with salt and pepper.

Divide the potato mixture into 12 balls. Flatten each ball into a patty that is about 1/2-inch thick.

Dredge the patties on both sides in flour, shaking off any excess. Place on a plate.

Heat 1/4 inch of oil in a large skillet over medium high heat. Once hot, add patties in batches, making sure not to overcrowd the pan as you work. Cook the patties for 3 to 5 minutes on each side, until golden brown.

Remove to a plate lined with paper towels and sprinkle with flaky salt. Repeat frying with remaining patties.

Serve warm with sour cream and chives or applesauce.