Score both sides of the white fish fillets with a knife and pat them dry thoroughly with paper towels.
Thinly slice the fresh ginger.
In a shallow pot or large pan, combine the water, sake, mirin, soy sauce, and sugar. Add the sliced ginger.
Bring the liquid mixture to a gentle simmer over medium heat.
Carefully place the white fish fillets into the simmering sauce. Reduce the heat to low.
Cover the pot with an otoshibuta (Japanese drop lid) or a piece of aluminum foil with a small hole in the center. Simmer for 10-12 minutes, basting occasionally with the sauce, until the fish is cooked through and flaky.
Once cooked, carefully transfer the fish fillets to serving plates. If the sauce is too thin, you can remove the fish and reduce the sauce slightly over higher heat until it thickens to your desired consistency.
Pour the simmered sauce over the fish. Garnish with thinly sliced green onion and serve immediately with steamed rice.
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