1Place all of the ingredients except the oil and salt in a medium bowl and stir to combine; set aside. Line a baking sheet with paper towels; set aside.
2Heat the oil in a large frying pan over medium heat until shimmering, about 3 minutes. Drop 3 to 4 (1/3-cup) dollops of the potato-cheese mixture into the pan and spread each into a 3-inch patty. Cook undisturbed until the bottoms are golden brown, about 4 to 5 minutes. Gently flip the cakes and cook until golden brown on the second side, about 4 to 5 minutes more. Transfer to the prepared baking sheet and season with salt. Repeat with the remaining potato mixture.