In a blender, combine the cubed watermelon and half of the diced cucumber. Blend until smooth.
Add the chopped red bell pepper, red onion, vegetable broth, lime juice, and olive oil to the blender. Blend again until fully incorporated and smooth.
Taste the gazpacho and season with salt and pepper as desired.
Pour the mixture into a large bowl and stir in the remaining diced cucumber and chopped mint leaves.
Cover the bowl and chill the gazpacho in the refrigerator for at least 1 hour to allow flavors to meld.
Serve the gazpacho chilled, drizzled with a little extra olive oil on top and, if desired, sprinkle with crumbled feta cheese for an added savory element.