Prepare the grill according to individual unit instructions. Adjust heat to medium. Brush the grill rack with a little oil. Brush the eggplant slices on both sides with about half a teaspoon per side of olive oil. Place on the grill, directly over the heat, and grill for about six minutes total, turning once with a spatula to cook on both sides. Remove and set aside.

Brush the tomato slices with olive oil and a little salt and pepper and place on the grill carefully. Grill for about 2-3 minutes per side. Remove and set aside. Turn off the grill.

Preheat the oven to 350 degrees Fahrenheit (180C). Oil the bottom and sides of six terrines, approximately three or four inches each in diameter. Fill each terrine in the following order: Place an eggplant slice, a tomato slice, a basil leaf and then the feta or mozzarella, repeat, and top with an eggplant slice. Press down lightly to fit into the terrines without being piled higher than the rim. Bake until the cheese melts, about 12-15 minutes. To serve, flip and turn out each terrine on a medium size plate. Drizzle with additional olive oil, if desired, or with the pesto sauce, diluted with a little olive oil.