In a large bowl, combine the mashed potatoes, 1 cup panko, and beaten egg. Shape the potato mixture into 3-inch patties. Dredge the patties in the remaining 1 cup panko.
In a large nonstick skillet over medium heat, add the vegetable oil. Add half of the patties and cook until golden brown, 2 to 3 minutes. Repeat the procedure with more oil, if needed, and remaining patties. Serve hot.
Boil the potatoes until done. Pour the potatoes into a medium bowl and add cream cheese and butter. Using a potato masher, mash the potatoes to desired consistency. Serve immediately.