Cut each melon into quarters lengthwise and remove the seeds with a large table or serving spoon. Square three of the quarters of each melon so they can be sliced easily. Run the remaining quarter of each melon through an electric vegetable juicer and reserve for tamari/melon sauce. Slice the squared quarters very thinly. Place in a mixing bowl with the Vidalia onion, mint leaves, cilantro leaves, yuzu, and lemon oil. Toss to combine and set aside.
Combine the broth, miss, and tamari in a medium sauce pot over medium heat. Simmer then add the salmon fillets. Return to a simmer and cook the fillets until they are just done, approximately 6 to 8 minutes, depending on the thickness of the fillets. Remove the salmon from the seasoned broth and allow to cool. Brush the fillets with the 2 remaining tablespoons of light miso. Store up to 4 hours.
Combine the melon juice and the tamari in a small sauce pot over medium-low heat. Light foam will form on the top of the sauce once it begins to simmer. Skim the foam and simmer two to four minutes. Remove from the heat and strain through a fine mesh strainer.
To assemble the dish, divide the melon salad onto the center of each of four chilled plates. Plate a salmon fillet atop each salad. Dress each fillet with some of the tamari/melon sauce. Serve immediately.
Recipe courtesy of Michel Nischan, Heartbeat Restaurant, New York, NY