8 ripe medium beefsteak tomatoes
2 ripe peaches pitted and cut into 1/2-inch pieces (2 cups)
3 Kirby cucumbers, peeled, seeded, and cut into 1/2-inch pieces (1 1/3 cups)
Kernels from 2 ears corn (1 1/2 cups)
6 tablespoons extra-virgin olive oil
1 to 2 tablespoons fresh lime juice
1 1/4 teaspoons coarse salt, plus more to taste
1/4 teaspoon freshly ground pepper, plus more to taste
1/2 cup shredded fresh basil leaves, plus sprigs for garnish