1. Quarter 4 peaches and 2 tomatoes. Process quartered peaches and tomatoes and next 2 ingredients in a food processor until smooth.
2. Chop remaining peach and tomato. Stir into pureed mixture. Season with kosher salt and freshly ground white pepper to taste. Cover and chill 1 hour.
3. Meanwhile, combine cucumber and next 3 ingredients in a medium bowl. Season with kosher salt and freshly ground white pepper to taste. Cover and chill 1 to 24 hours. (Chilling can dull the seasoning, so you may need to add more salt and pepper before serving.)
4. Ladle gazpacho into bowls. Spoon cucumber mixture over gazpacho. Drizzle each serving with about 1 tsp. extra virgin olive oil. Serve immediately.