Preheat the oven to 400 degrees F.
Fill a large bowl with water and set aside.
Grate the potatoes on the side of a box grater. Add the grated potatoes to the bowl filled with water and let the potatoes soak for 5 minutes to release their starch.
Drain the potatoes into a colander and press out any excess liquid. Squeeze the grated potatoes between your hands to remove as much excess water as possible and then add them to a large mixing bowl.
Add the egg, flower, salt, pepper, scallions, and cayenne pepper into the potatoes and then mix everything to combine. The potato mixture will be sticky from the flour and egg, which will allow you to form them into patties.
Scoop 1/3 cup of the potato mixture and place it onto a parchment-lined baking tray. Press the potato mixture together into a tight patty and repeat for the remaining potato mixture. You can also form it between your hands before placing it on a parchment-lined baking tray as well.
Once all the patties have been formed, drizzle each of them with some vegetable oil.
Place the hashbrowns into the oven and bake for 40-45 minutes, flipping the hashbrowns halfway through cooking. Once they are done, they will be nice and golden brown and crispy.
Serve warm with some extra salt and some ketchup to dip. Enjoy!