Grate the peeled potatoes using a box grater and transfer them to a clean kitchen towel.

Wrap the grated potatoes in the towel and squeeze out as much moisture as possible.

In a large bowl, combine the dried grated potatoes, beaten egg, flour, salt, and pepper. Mix until well combined.

Form the mixture into 8 equal-sized patties, about 1/2 inch thick.

Heat a large skillet over medium-high heat and add enough vegetable oil to cover the bottom.

Once the oil is hot, add the patties to the skillet without overcrowding. Cook until golden brown and crispy, about 4-5 minutes per side.

Transfer the cooked patties to a paper towel-lined plate to drain any excess oil.

Serve the hash brown patties hot and enjoy!