Bring a small saucepan of water to a boil. Add the basil to the boiling water and cook until just wilted and bright green, about 15 seconds. Transfer with a slotted spoon to a blender and puree until smooth. With the machine running, add the olive oil and 1/4 teaspoon each salt and pepper.
Spread the basil puree on a serving platter. Arrange the peaches and tomatoes on top and sprinkle with the lemon juice, 1/4 teaspoon salt and 1/8 teaspoon pepper. Garnish with whole basil leaves and serve.