Clean fish head, bones, and tail, pat dry, coat evenly with flour or starch, and sprinkle with salt.
Heat a pan to high temperature, add oil, fry fish bones until golden. Add kelp, ginger slices, and garlic, then add pasta water, bring to a boil, cover, and simmer on low heat for 15 minutes.
Add cooked pasta, milk, and vegetables to the fish soup.
When the soup boils, turn off the heat, soak fish fillets for 4 more minutes. Done!