Steps

Peel the potatoes and quarter into equal chunks for quicker, more equal cooking. Add to a pot of water with enough liquid to cover the potatoes. Bring to a rolling boil and cook until you can easily pierce the potato with a fork ~20 mins

saute the onion with butter over medium heat until the onion is golden brown. Add ground beef and season with salt and pepper. Brown the beef and add the soy sauce, mirin, and sake if using and cook util the liquid is cooked off. Set aside until the potato is done cooking

when the potatoes are ready, drain the water and let them sit for a minute so they can dry out. A drier potato mixture helps the patty hold its shape during frying and creates a crispier outside. Mash the potatoes and mix with the onion beef mixture. Add the sugar, salt, and pepper to taste

Form the potato mixture into 6 oval patties ~2cm thick. Place them on a tray and let them chill in a fridge. Chilling helps the patties keep there form and make them less likely to break apart or lose shape

make a dredging station with the flour, eggs, and breadcrumbs. Dredge each patty by coating with flour, then eggs, then breadcrumbs

add oil to a pot and bring to 350ºF over medium heat. Deep fry croquettes until both sides are golden brown ~3 mins

transfer to a wire rack or a plate lined with paper towels to drain the excess oil

optionally server with tonkatsu sauce and/or shredded cabbage