Preheat your barbecue or indoor grill to medium-high.
Lightly brush the eggplant with the 2 Tbsp. oil and season with salt and pepper. Grill eggplant two minutes per side, or until nicely coloured and just tender. Set the eggplant on a plate and cool to room temperature. Carefully spread one side of eight of the eggplant slices with goat cheese. Now spread those slices with pesto, and then set a tomato slice on each of them. Stack two of the tomato topped eggplant slices together and set on a plate. Repeat with the remaining topped eggplant slices. Top each stack with one of the remaining slices of grilled eggplant. Drizzle with olive oil and balsamic vinegar and serve.