Line a baking sheet with parchment paper. Set it aside.
Bring a medium pot of salted water to a boil.
Add the halved potatoes and parboil for 6 minutes. The potatoes should be partially cooked but not fully tender.
Drain the potatoes and let them cool slightly until they are comfortable to handle.
Using a box grater, grate the parboiled potatoes.
In a large bowl, combine the grated potatoes, eggs, flour, and kosher salt. Mix until well combined.
Divide the potato mixture into 8 equal portions, forming each into a patty. You can shape them into rounded rectangles or any shape of your choice.
Place the formed patties on the prepared baking sheet.
Freeze the patties for 45 minutes to 1 hour. This step is crucial for the patties to hold their shape during frying.
Heat the oil in a large skillet over medium-high heat until it reaches 350°F.
Add 1-3 patties to the hot oil at a time, frying each for 3-5 minutes on one side until browned.
Flip the patties and cook for another 3-5 minutes until the other side is browned and the patties are cooked through.
Transfer the fried patties to a paper towel-lined baking sheet to drain excess oil.
Ensure the oil is at 350°F for each batch and repeat the frying process with the remaining patties.
Serve the hash brown patties hot.