Watch chef Shea Gallante's video demonstration of how to make this recipe. Cold Soup Recipes
In a blender, puree half of the watermelon cubes. Strain the watermelon juice through a fine sieve set over a large glass or stainless steel bowl. Add the remaining watermelon and the tomatoes, cucumber, bell pepper, onion, garlic, red wine and Champagne vinegars and a 1/2 tablespoon of the lemon juice. Season lightly with salt and pepper and refrigerate for at least 6 hours or overnight.
Transfer the mixture to a blender and puree until smooth. With the machine on, slowly pour in 1/4 cup of the olive oil. Strain the soup into a bowl through a fine meshed sieve, pressing hard on the solids to extract as much liquid as possible. Discard the solids. Season the gazpacho with salt and pepper.
In a small bowl, toss the lobster with the remaining 1/2 tablespoon of lemon juice and 1 tablespoon of olive oil; season with salt and pepper. Ladle the gazpacho into shallow soup plates. Mound the lobster in the center of each soup and top with a few slices of avocado. Garnish with the tarragon and mint and serve immediately.