Grilled Lamb with Tomato Vinaigrette & Caponata

Ingredients

• 1 large eggplant (about 2 pounds), cut into 1-inch cubes
• Kosher salt
• 6 celery ribs, cut into 1-by-1/4-inch matchsticks
• 1/2 cup plus 3 tablespoons extra-virgin olive oil
• 3 garlic cloves, finely chopped
• 6 basil leaves, finely chopped
• One 28-ounce can crushed tomatoes
• 1 large onion, very finely chopped
• 1 cup pitted green olives, thinly sliced
• One 3-ounce bottle brined capers—drained, rinsed and patted dry
• 1/2 cup white wine vinegar
• 3 tablespoons sugar
• 1/2 cup extra-virgin olive oil
• 1 large tomato, chopped
• 1 tablespoon tomato paste
• 2 tablespoons finely chopped tarragon
• 1 tablespoon finely chopped parsley
• 1/2 lemon—very thinly sliced, seeds removed
• 1 tablespoon white wine vinegar
• 1 tablespoon fresh lemon juice
• Salt
• Freshly ground white pepper
• 2 frenched racks of lamb (2 1/2 pounds each), cut into individual chops
• Extra-virgin olive oil, for rubbing
• Freshly ground black pepper
• Grilled bread, for serving
• 6 ounces sheep-milk feta cheese, crumbled, for serving
• Agrodolce Caponata, for serving