Peel the cucumber. (If you are using an English or hothouse cucumber, you do not need to peel it.)
Seed the cucumber by cutting it in half lengthwise and scooping out the seeds and gelatinous pulp with a spoon. Chop.
Remove the core of the tomato by inserting a knife at an angle around the stem-end and removing the core. Chop.
Place all ingredients in a blender and puree until the mixture is smooth.
Cover and refrigerate until chilled or ready to serve.
To serve, spoon the gazpacho into bowls and garnish with cut up cucumber and basil if desired.
Tips: To serve watermelon gazpacho as a starter or appetizer, pour into shot glasses or small glasses and serve as shooters.Watermelon Gazpacho can be served immediately, but it is better if allowed to chill at least 30 minutes.Even seedless watermelon have a few small seeds. Don't worry about trying to remove them.[nutrition-label]