Preheat the oven to 375 degrees F. Cut 4 large squares of heavy aluminum foil large enough to hold 1 flounder fillet and one-quarter of the vegetables. Lightly butter 1 side of each and set on a work surface.
Lay the fish flat in a baking dish. In a bowl, whisk together the sake, soy sauce, lime juice, ginger, sesame oil, honey, and sesame seeds. Pour over the fish and let marinate for up to 30 minutes. Arrange 1 fish fillet on each sheet of aluminum foil and top with one-quarter of the mushrooms, onions, carrots, peppers, and marinade.Wrap tightly and place on a baking sheet. Bake until the fish is cooked through and the vegetables are tender, 15 to 20 minutes. Remove from the oven and unwrap each package. Transfer the fish and vegetables to 4 large plates and top with the cooking juices. Serve with Sauteed Shiitakes and hot steamed rice.
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