Boil the Potatoes
Begin by bringing a medium pot of water to a rolling boil. While the water heats, peel, wash, and quarter the potatoes. Carefully place the potatoes into the boiling water and cook until they are tender and easily pierced with a fork, approximately 20 to 25 minutes. Drain the cooked potatoes thoroughly in a colander. Return them to the pot while still warm, mashing them until smooth. Incorporate the butter into the mash, ensuring it melts fully, and set the mixture aside.
Cook the Filling
As the potatoes cook, prepare the filling. Heat one tablespoon of oil in a skillet over medium heat. Sauté the minced onion, stirring frequently, until softened, about 3 to 4 minutes. Add the ground beef to the skillet, breaking it into small pieces as it cooks. Stir in the soy sauce, granulated sugar, and black pepper. Continue cooking until the beef is fully browned, which should take another 3 to 4 minutes.
Combine and Cool
Transfer the beef mixture into the pot of mashed potatoes, stirring thoroughly to blend. Taste the mixture and adjust seasoning with salt and additional pepper, if necessary. Allow the mixture to cool slightly until it reaches a warm, manageable temperature.
Shape the Patties
Using your hands, form the potato mixture into oval-shaped patties, roughly 1 inch thick and 3 inches long. Arrange the formed patties on a baking sheet. This recipe should yield approximately 10 to 12 patties. Cover the patties loosely with plastic wrap and refrigerate for at least 30 minutes to firm up.
Prepare the Breading Station
While the patties chill, set up the breading station. Spread the flour on one plate, beat the eggs in a shallow bowl, and place the panko breadcrumbs on a second plate.
Bread the Patties
Remove the chilled patties from the refrigerator. Dip each patty first into the flour, ensuring it is completely coated. Next, submerge the floured patty into the beaten eggs, covering it evenly. Finally, roll the patty in the panko breadcrumbs until fully coated. Place the breaded patties back onto the baking sheet.
Deep-Fry the Korokke
Heat enough oil in a medium saucepan to reach a depth of 1½ inches. Warm the oil to a consistent temperature of 340°F. Fry the patties in small batches, typically two at a time, to prevent the oil temperature from dropping too much. Fry for about 3 minutes, flipping once, until the patties achieve a golden-brown color. As they are already cooked inside, their color serves as an indicator of doneness. Remove the korokke and place them on a wire rack or a plate lined with paper towels to drain excess oil. Repeat this process with the remaining patties, monitoring the oil temperature throughout to ensure consistency.
Serve and Enjoy
Serve the korokke while still hot, optionally accompanied by tonkatsu sauce for added flavor.