In a large bowl, whisk together oil and lemon juice; season with salt and pepper. Add tomatoes, cucumber, fennel, onion, and olives. Toss to combine. Refrigerate for at least 1 hour and up to 4 hours.
Heat broiler with rack set 4 inches from heat. On a baking sheet, toast bread until light brown on both sides, 1 to 2 minutes a side. Place the bread on a work surface and rub cut side of garlic against bread. Discard garlic. Cut bread into 2-inch pieces.
To serve: Place bread in four shallow bowls. Top with tomato salad and scatter basil and cheese over top.
Choose a mix of many-colored heirlooms for this Italian bread salad, also known as panzanella. Although traditional recipes call for adding the bread at the beginning, saving it until the end keeps it soft but not mushy.