Preheat barbecue, brush grids with vegetable oil and set on LOW.
Prepare eggplant by covering slices with coarse salt for 20 minutes.
Rub off salt with a paper towel and pat dry. This removes the bitterness of the eggplant.
Brush bottom of eggplant slices with a mixture of olive oil and garlic. Place on grids and cook for 8 minutes.
Turn slices over and spread top of each eggplant slice with a teaspoon of pesto.
Cover with diced tomatoes, mozzarella cheese and parmesan cheese.
Return to grill and cook a further 5 - 7 minutes. Garnish with fresh basil.