Salt the mackerel fillets generously on both sides and place on a plate in the refrigerator for 30 minutes.

Simmer the daikon in a small pan of water until tender, about 5 minutes. Rinse under cold water and set aside.

Bring a large pan of water to a boil and reduce to a simmer. Fill a large bowl with cold water. Slice the mackerel into 1-inch squares. Dip the fish, a few pieces at a time, into the simmering water for 15 seconds to blanch, then transfer to the cold water. When you've blanched all the fish, drain it and dry on paper towels.

Combine the dashi, 2 cups water, sake, and miso in a bowl and whisk to blend.

Place the cabbage on the bottom of a large stockpot. Add the tofu, daikon, and oyster mushrooms, arranging each ingredient in a neat bunch. Pour in the broth.

Cover the pot and bring to a boil over high heat. Uncover, reduce heat to medium-low, and add the mackerel in a separate pile. Simmer ten minutes, reducing heat further if necessary to maintain a low simmer.

Serve in individual bowls, garnished with grated ginger and optional scallions.