Wash and peel 230 g potatoes. Cut them into evenly sized pieces and place them in a pot of cold water with a generous pinch of salt. Bring to a boil and cook until fork-tender (10-15 minutes depending on the size).
Once soft enough for a fork to slide through with ease, drain the potatoes and place them in a large heatproof mixing bowl. Mash them while hot until smooth.
Rest until it's cool enough to touch (about 5-10 minutes), then add 3 tbsp preferred shredded melting cheese, 2 tbsp potato starch (katakuriko), 1 tbsp grated parmesan cheese, ½ tsp sugar and ¼ tsp salt.
Knead by hand until the ingredients are evenly distributed and the dough is smooth with a soft play-doh texture. See notes for troubleshooting.
Divide the dough into 5 equal pieces, then roll each piece into a patty shape about 1-1.5cm (½") thick and 6-8cm (approx 3") in diameter.
Drizzle 1 tsp cooking oil into a cold frying pan and place the patties spaced apart. Place ½ tbsp butter in the center and heat over medium-low.
Once they start to sizzle, cook for about 4-5 minutes or until a golden crust forms, then flip and repeat on the other side. Once golden on both sides, add 1 tbsp of water to the pan and cover with a lid. Steam for about 1 minute, then remove the lid and allow the excess moisture to evaporate before taking the pan off the heat.
Add 1 tbsp Japanese soy sauce (koikuchi shoyu), 1 tbsp mirin and 1 tbsp sugar to a small saucepan. Heat over medium while stirring continuously until the mixture reaches a slightly thickened, syrup-like consistency.
Immediately pour the sauce over the potato mochi. Enjoy!
Notes
Start with cold water when cooking potatoes to ensure they cook evenly.
If the dough is cracking or feels crumbly, add a few drops of water and knead again. Repeat until the texture is soft and pliable.
If the dough is too sticky, try adding extra potato starch 1 tsp at a time. Alternatively, let it cool more to make it easier to handle.