Add water and potatoes to a large pot, cover, and bring to a boil over medium heat, leaving the lid slightly ajar to prevent boil-overs. This takes about 15 minutes. Reduce heat to maintain a gentle simmer and cook until tender, 15 to 20 minutes.
Meanwhile, preheat a large skillet over medium heat, then add the oil.
0.5 tablespoon neutral oil
Add the sliced onion.
0.5 onion
Sauté the onion until translucent, tender, and lightly caramelized, about 10–15 minutes. Take care not to burn it. Tip: Make sure no moisture remains in the onion so the croquettes don't turn soggy. Let the onion sit a bit longer between stirs to build deeper color.
Add the ground beef to the pan and break it up with a wooden spoon.
250 g beef
Season with salt and pepper.
0.25 teaspoon salt, 1 pinch black pepper
Stir to combine and cook until the meat is no longer pink. Turn off the heat and set the pan aside to cool slightly.
Check the potatoes for doneness. Insert a skewer into a larger piece; if it slides in easily, they're done. Remove from the heat and drain thoroughly. Use the lid to keep the potatoes from falling out of the pot.
Return the pot to low heat. Shake the pot gently and let any remaining moisture evaporate completely without browning the potatoes, 2 to 3 minutes. Transfer to a large bowl.
Using a potato masher, mash the potatoes while still hot, letting the steam escape as you work. Add the butter.
0.5 tablespoon butter
Add the salt and black pepper and mix well.
0.25 teaspoon salt, 1 pinch black pepper
Gently press out the liquid from the meat mixture by gathering it to one side of the pan to avoid excess moisture in the croquettes.
Add the drained meat mixture to the bowl with the mashed potatoes and stir to combine.
To form the croquettes
While the mixture is still warm (not hot), shape into oval croquettes about 7.5 cm long. Avoid creating air pockets.
Place the croquettes on a tray or plate. Cover and chill the Korokke in the refrigerator for 15 to 30 minutes. Don't skip this step! Tip: Chilling prevents the croquettes from bursting during frying. If they're cold, they won't build up steam that can rupture the coating. Resting also helps the ingredients meld.
To bread the croquettes
Set up one dish for the flour and another for the panko. Crack the eggs into a small bowl and beat with a fork.
40 g flour, 60 g panko breadcrumbs, 2 eggs
Coat each Korokke in flour, shaking off the excess.
Dip in the egg, then coat with panko, pressing so the crumbs adhere.
For frying
When all the croquettes are breaded, add neutral oil to a medium pot. Ensure there is at least 5 cm of oil so the croquettes can be fully submerged.
Oil
Heat the oil to 170–180°C over medium heat. Fry 2 to 3 croquettes at a time until golden, 2 to 3 minutes. Tip: Don't move the croquettes until one side is golden. The centers are already cooked; you're just frying to color and crisp.
Transfer to a rack or a paper towel–lined plate to drain excess oil. Repeat with the remaining croquettes.
To serve
Serve the Korokke with tonkatsu sauce drizzled in a zigzag on top.
Notes
Make sure no moisture remains in the onions so the croquettes don't turn soggy. Let the onion sit a bit longer between stirs to build deeper color.