Place cauliflower, shallots, sugar, and salt in a large bowl; toss to coat. Let stand 30 minutes.
Preheat grill to medium-high (about 450°F).
Generously coat eggplant with cooking spray. Place in a single layer on oiled grill grates; grill, covered, until tender, 5 to 6 minutes, turning occasionally. Cut into 1-inch cubes. Add eggplant, tomatoes, basil, vinegar, oil, capers, and olives to cauliflower mixture; toss well. Let stand 10 to 15 minutes. Serve with a slotted spoon.