The day before, stir the sugar into the milk until dissolved, pour it into a shallow, flat container — a small baking dish works well — and freeze it solid overnight.
If using canned red beans, taste them; add a pinch more sugar if they're mild, or leave as is.
To shave the frozen milk, run the underside of a heavy metal spoon firmly across the surface, working in short strokes, to scrape off fine, snow-like flakes into a bowl. Alternatively, break the frozen block into rough chunks and pulse them in a food processor in short bursts until they turn to snow rather than slush.
Mound the shaved milk ice into two wide, shallow bowls.
Spoon the sweetened red beans generously over the top of each mound.
Scatter the rice cake cubes and fruit, if using, over the beans.
Drizzle with condensed milk and dust with roasted soybean powder.
Serve immediately with a long spoon, and mix everything together before eating rather than eating it in layers.