Toss cherry tomatoes with oil and salt and pepper on a baking sheet with sides. Roast the tomatoes for 20 minutes in the oven until they start to split open and brown. Remove from the oven and set aside.
Salt both sides of the eggplant lightly. Let sit for 20 minutes.
Meanwhile, put cauliflower florets into a microwave-safe container with one tablespoon of water. Cover with plastic wrap and microwave on high for 2 minutes. Drain and toss with olive oil and salt and pepper. Grill until charred, turning often10-12 minutes. We use a grill basket for this.
Toss the cauliflower with the sugar in a large bowl and set aside for 30 minutes.
Spray the eggplant on both sides evenly with cooking spray. Grill over evenly spread coals for 5 to 7 minutes on each side, until soft and brown. Remove and place in a pan in a single layer. Cut into 1-inch pieces.
Combine the tomatoes and eggplant with the cauliflower in the bowl. Stir in the vinegar, olive oil, basil, and capers. Let stand for 10 minutes, adjust salt and pepper, and serve.