Place the watermelon chunks into a blender and blend. Add the cucumber, salt, pepper, basil and vodka and blend. Chill the soup for at least 3 hours until ready to serve.
Before serving, take a skewer and place one piece of leftover watermelon, one piece of feta and the another piece of watermelon.
Pour the soup into chilled bowls or martini glasses and serve with one skewer.