Using a box grater, grate the potatoes then transfer them to a bowl of ice water and let it sit for 20 minutes.
Drain the water and squeeze out as much moisture from the potatoes as possible.
Add butter to a non-stick pan and place over medium heat. Add the shredded potatoes and cook for 15 minutes.
Transfer the potatoes into a bowl and let it cool slightly. Once cool, add the remaining ingredients until a thick dough remains. If the dough is too thick, add a splash more water.
Using your hands, shape the mixture into rectangular hash browns. Transfer them to a lined plate and refrigerate for at least two hours.
Add an inch of oil to a non-stick pan or pot. Once hot, add the chilled hash browns and cook for 2-3 minutes on each side, or until golden.
Place the cooked hash browns on a wire rack until ready to serve.