In a large mixing bowl, combine the leftover mashed potatoes, shredded turkey, shredded cheddar cheese, chopped green onions, and fresh parsley.
Crack the egg into the mixture and sprinkle in the garlic powder, onion powder, black pepper, and salt. Mix all ingredients together until well combined. The mixture should be thick and moldable.
Using your hands, scoop about 0.25 cups of the mixture and form it into a patty shape. Repeat until all the mixture is used, placing the formed cakes on a parchment-lined tray.
Take the breadcrumbs and spread them out on a plate. Dredge each potato cake in breadcrumbs, pressing lightly to ensure they stick well. Set aside.
In a large skillet, heat the olive oil over medium heat until shimmering. Make sure the oil is hot enough to create a sizzle when you add the cakes.
Carefully place the potato cakes into the skillet, ensuring not to overcrowd the pan. Fry for about 4-5 minutes on each side, or until golden brown and crispy.
Once cooked, transfer the cakes to a paper towel-lined plate to drain any excess oil.
Serve the cheesy potato cakes warm with a side of sour cream or your favorite dipping sauce.