Pass the potato through a sieve while hot, then add the milk.
Add the katakuriko and mix well. Once evenly combined, shape them into small oval patties.
Place the patties in a frying pan with melted butter, season with salt and pepper, and fry until golden brown over low heat. Flip them over and brown the other sides.
I also tried it with sweet potatoes, which were also tasty as expected. Adjust the recipe depending on the size of the sweet potato.
While frying them in butter is tasty, I also recommend coating them in a mixture made of 1 part sugar to 1 part soy sauce, then baking them on a sheet of greased aluminium foil.
After about 5 minutes, they'll resemble mitarashi dango. What's more is that they're oil-free and fuss free, since clean up is easy.
The photo in Step 5 also shows a mitarashi dango style version.
Here is a curry flavored version. Use the proportion of 1/2 teaspoon curry powder to 1 teaspoon soy sauce for each potato.
Story Behind this Recipe
I had these potato mochi at a friend's house, and tried to replicate them and came up with this recipe. I based this on the popular method using katakuriko.
Although it is time consuming, the texture of the potato is best when strained through a sieve. Add milk until it reaches a cream-like consistency, then add just enough katakuriko to make them firm enough to shape into balls. If you use tapioca powder instead, they will become even springy and chewier.