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

Instructions

1. Cut all tomatoes into 1/3-inch cubes; place in large bowl. Add 1 teaspoon fleur de sel; toss. Let stand 15 minutes. Transfer tomatoes to strainer set over large bowl; let stand 45 minutes to drain well, tossing often. Transfer tomatoes to medium bowl; stir in chopped basil, 1 tablespoon olive oil, garlic, and shallot. Season with fleur de sel and ground black pepper.
2. Line six 3/4-cup ramekins or custard cups with plastic wrap, leaving long overhang. Fill each ramekin with scant 1/2 cup tomato mixture; press to compact. Cover with plastic overhang, pressing firmly. DO AHEAD: Can be made 2 hours ahead. Let stand at room temperature.
3. Prepare barbecue (medium-high heat). Open up plastic wrap on ramekins. Invert 1 ramekin onto each of 6 plates, releasing tomato mixture. Brush shrimp with olive oil; sprinkle with fleur de sel and pepper. Grill shrimp, shell side down, 1 1/2 minutes. Turn shrimp over and grill just until opaque in center, about 1 1/2 minutes longer. Arrange 2 shrimp halves atop tomatoes on each plate. Drizzle remaining 1 tablespoon olive oil over tomatoes, garnish with whole basil leaves, and serve.