In a large bowl, mix together the mashed potatoes, egg, flour, cheese, green onion, salt, and pepper.
Place a large skillet over medium-high heat. Add 1 tablespoon olive oil and 1/2 tablespoon butter into the skillet.
Once the butter is melted, add large spoonfuls of the potato mixture to your skillet. Do not overcrowd the pan, you'll work in 2 batches.
Brown the pancakes on each side until they are golden, using a spatula to flip them once. Transfer pancakes to a plate. Add the remaining oil and butter to the skillet and repeat with the remaining potato mixture.
I like to serve these potato pancakes topped with sour cream and a little more green onion.