Line a baking sheet with parchment paper. Set aside.
Bring a medium pot of salted water to a boil.
Add potatoes and parboil (partially cook) for 6 minutes. (The potatoes won't be cooked through.)
Allow potatoes to cool slightly, or enough to comfortably hold. Then, grate the potatoes using a box grater.
In a large bowl, add grated potatoes, eggs, flour, and salt. Mix well.
Form into 8 equal patties (about 3-4 ounces each). We made our patties into rounded rectangle shapes; you could make them the shape of your choice.
Place the patties on the lined baking sheet and freeze for 45 minutes to an hour. (Don't skip this step!)
When ready, heat oil to 350°F in a large skillet over medium-high heat.
Add 1-3 patties at a time and cook 3-5 minutes, or until browned. Flip the patties and cook another 3-5 minutes. Baste with oil on both sides while frying. Place hash brown patties on a paper towel-lined baking sheet to soak up excess oil.
Repeat with the remaining patties, making sure the oil is at 350°F for each batch.
Serve patties hot.