Reserve 2 tablespoons of the mint. Place the remaining mint in a large bowl along with the cucumbers, 2 cups watermelon, yogurt, onion, cilantro, lemon juice, ginger, cayenne pepper and 2 teaspoon salt. In small batches, puree in a food processor until smooth. Place in a pitcher or large bowl and refrigerate for 2 hours.
Taste the gazpacho before serving and season with additional salt if needed. Divide the soup among 6 chilled bowls and top with the feta, toasted pepitas, remaining watermelon, reserved mint and a drizzle of chili infused oil.