Blend the ingredients together in a blender until pureed. See notes for preferred order (hardest veggies first, then the juices and olive oil, followed by the seasonings.
Taste, season with salt and pepper if desired and chill in the refrigerator until time to serve.
You will want to chill the gazpacho for 2-3 hours before serving, so plan ahead!
Pour into serving cups or bowls, and garnish with mint leaves, feta cheese, and additional chopped watermelon and veggies.