For tomato vinaigrette, purée tomatoes in a food processor, pass through a fine sieve into a bowl (discard seeds and skin), stir in olive oil and vinegar and season to taste.
Preheat a char-grill over medium-high heat. Brush eggplant slices with olive oil and grill, in batches, turning once until cooked through (4-5 minutes each side).
Increase char-grill to high heat, brush haloumi with olive oil, grill until golden (1-2 minutes each side). Arrange with eggplant on serving plates, drizzle with vinaigrette, scatter with mint and serve immediately.