In a large bowl, grate all of the peeled potatoes using the star grater side of a box grater (protect your hands with safety gloves!) Use a spoon to scrape off any excess liquid on top (remove about 1/3 cup).
In the same bowl, grate a medium-sized onion on the same side as the star grater (no need to wash the grater). Reserve 1 tablespoon of grated onion and set aside for the meat mixture.
In the potato and onion mixture, add 1 large egg, 3 tablespoons flour, 1 tablespoon sour cream, 1 teaspoon salt and 1/8 teaspoon black pepper. Stir until combined and set aside.
In a medium bowl, combine 1/2 pound ground beef with 1/4 teaspoon salt, a pinch of black pepper, and 1 tablespoon grated onion. Mix until well blended. Divide the meat into 16 thin pieces, each about 2 inches wide and set aside.
Heat a large non-stick frying pan* over medium heat with 2-3 tablespoons of oil. Once the oil is hot, add the potato mixture 1 tablespoon at a time, flattening the top with the back of a spoon. Immediately place a piece of meat on each patty and cover each with another tablespoon of the potato mixture**. Fry 4 minutes per side or until fully cooked through and golden brown. Transfer to a plate lined with paper towels and serve immediately. Repeat the process with the rest of the ingredients, adding more oil as needed.