Wash 2 lb russet potatoes under cold running water. Peel them and remove the eyes. Cut each potato into 4 equal pieces so they cook evenly.

Put the cold running water and potatoes in a large pot and cover with a lid slightly ajar to prevent boiling over. Turn on the heat to medium and bring it to a boil; this will take about 15 minutes. Once boiling, reduce the heat to maintain a gentle boil and cook until done, about 15–20 minutes.

Meanwhile, prepare the onion and ground beef. Mince 1 onion finely. Preheat a large skillet on medium heat. Once it's hot, add 1 Tbsp neutral oil and the minced onions. Sauté until translucent and tender, about 12–15 minutes. Add 1 lb ground beef to the pan and break it up with a wooden spoon. Season with ½ tsp Diamond Crystal kosher salt and ¼ tsp freshly ground black pepper. Stir andcook until the meat is no longer pink.

To check if the potatoes are cooked, insert a skewer into a bigger piece; it's done if it pierces easily. Remove from the heat. Drain off all the water. Move the pot back to the stove over low heat. Continuously shake the pot to evaporate the remaining moisture from the potatoes, about 1–2 minutes. Transfer them to a large bowl.

Mash the potatoes with a potato masher while they are still hot. Add 1 Tbsp unsalted butter, ½ tsp Diamond Crystal kosher salt, and ¼ tsp freshly ground black pepper and combine gently. Add the drained meat to the bowl of potatoes and gently mix to combine.

While the mixture is still warm, form oval-shaped patties 3 inches in length. Place the patties on a tray or plate to let cool completely. Once cool to room temperature, cover and rest them in the refrigerator for 15–30 minutes.

Prepare separate trays for ½ cup all-purpose flour and 2 cups panko. Crack 3 large eggs into a small bowl and beat with a whisk. Dredge each patty in flour, dip in the beaten egg, then coat with the panko.

Add 4 cups neutral oil to a medium pot and bring it to 340–350ºF over medium heat. Deep-fry 2–3 croquettes at a time until golden brown, about 2–3 minutes. Transfer to a wire rack or a plate lined with paper towels to drain the excess oil.

Serve with tonkatsu sauce.