Combine Ingredients: In a large bowl, combine mashed potatoes, cheddar cheese, onion, eggs, flour, breadcrumbs, salt, and pepper. Mix well until all ingredients are evenly distributed.
Form Patties: Divide the mixture into 4 equal portions and shape each portion into a flat, round patty.
Cook: Heat olive oil or butter in a large skillet over medium heat. Cook the potato cakes for 3-4 minutes per side, or until golden brown and crispy.
Serve: Serve hot, garnished with chopped chives or green onions, if desired.