Drain the tofu thoroughly. Wrap in paper towels and press under a weight for 20–30 minutes — this is the most important step.
Cut the drained tofu block into four equal pieces, keeping them large so they hold together.
Spread potato starch on a tray and coat each piece of tofu on all sides, patting gently to make it stick.
Heat oil 1–2cm deep in a frying pan over medium-high heat. Shallow-fry the tofu, turning, until golden and crispy on all sides — about 5–7 minutes total.
Transfer the fried tofu to a wire rack to drain.
Combine water, dashi granules, mirin, and soy sauce in a saucepan. Bring to a simmer until the dashi dissolves.
Place two pieces of tofu in each bowl. Pour the warm broth around them. Top with grated daikon and sliced green onions. Serve immediately.