
Make the batter: In a large mixing bowl, combine the mashed potatoes, feta, flour, scallions, egg, and parsley. Mix with a wooden spoon until everything is well incorporated.
Make the mashed potato patties: Spread the breadcrumbs on a plate. Scoop the potato mixture using a measuring cup (1/4 cup or 1/3 cup, depending on what size pancakes you want). Form the scoop into a ball, then lightly flatten to make a 1/2-inch thick patty. Coat the patty on both sides with the breadcrumbs, then set it flat on a baking sheet. Repeat with the remaining mashed potato mixture, replenishing the breadcrumbs as necessary.
Fry the mashed potato pancakes: Line a tray with paper towels and set near your stove. Set a large non-stick pan or skillet over medium-high heat. Add enough olive oil to the pan so it's about 1/2-inch deep. When the oil shimmers, arrange the patties in the pan in one single layer (do this in batches, if needed). Cook until crispy and golden on both sides, about 2 to 3 minutes per side. Set the cooked pancakes aside on the prepared tray as you go.
Finish and serve. Transfer the mashed potato patties to a serving plate and garnish with a bit more feta cheese and scallions. Enjoy!