Grilled Shrimp with Cherokee and Oxheart Tomato Tartare

Name: Grilled Shrimp with Cherokee and Oxheart Tomato Tartare
Ingredients: 2 Giant Oxheart tomatoes (about 12 ounces total); 2 Cherokee Purple tomatoes (about 12 ounces total); 1 teaspoon fleur de sel or coarse kosher salt plus additional for sprinkling; 2 tablespoons coarsely chopped fresh opal or green basil plus additional whole leaves for garnish; 2 tablespoons extra-virgin olive oil (preferably Ligurian), divided, plus additional for brushing; 1 garlic clove, minced; 1 teaspoon minced shallot; 6 uncooked unpeeled jumbo shrimp (about 2 ounces each), cut in half lengthwise through shell, deveined, shell still attached