Cut eggplant into ¾ in. (2 cm) thick slices. If desired, peel the eggplant lengthwise in stripes, leaving part of the skin. Set aside.
In a bowl, combine cherry tomatoes, shallots, 30 mL (2 tbsp) olive oil, red wine vinegar, basil, salt and pepper.
Place tomato mixture in an aluminium tray and cover with foil. Heat BBQ to high. Place on grill and cook for 10 to 15 minutes or until it reaches the consistency of a sauce.
Brush eggplant with remaining olive oil. Oil the grill and add eggplant slices. Close cover and cook for about 5 minutes or until golden. Flip them over and sprinkle with Mozzafina di latte / Mozzarina Mediterraneo cheese. Cook 4 to 5 more minutes or until bottom is golden and cheese melted.
To serve, top eggplant slices with tomato mixture.