In a large bowl, stir together the mashed potatoes, cheese, thyme, scallions, egg and 3 tablespoons flour until combined.
Divide the mixture into 12 portions. Roll each portion into a compact ball then flatten it into a pancake about a 1/2-inch-thick.
Place the remaining 1/2 cup of flour in a shallow dish and carefully dredge each pancake in the flour.
Heat 3 to 4 tablespoons of vegetable oil in a pan over medium heat.
Fry the pancakes, in batches, until they're golden brown and crispy on both sides, 3 to 4 minutes. Add more oil to the pan as needed between batches. (Do not overcrowd the pan and do not flip the pancakes too soon or they won't develop a crisp crust.)
Transfer the pancakes to a paper towel-lined plate. Dunk them in Mayo and you'll know why I called these the Tippy Toe Potato Pancakes