1. Preheat a grill to medium-high heat.
2. Place the eggplant rounds in a single layer on a rimmed baking sheet, and brush both sides with olive oil.
3. When the grill is hot, use tongs to place the eggplant rounds on the grill. Cook, covered and turning once, until the eggplant flesh is tender through the center, but not completely soft and limp, 4–5 minutes per side. Transfer the eggplant back to the baking sheet to cool. Sprinkle lightly with fine sea salt.
4. Line another baking sheet or your work surface with parchment, and place 10 of the largest tomato slices on top in a single layer. Sprinkle each with a small pinch of coarse or flaked sea salt. Next, top each tomato slice with a grilled eggplant round that is equal in size (or slightly smaller). Spread a small spoonful of pesto over each eggplant round and top it with a slice of mozzarella. Place smaller tomato slices on top of the mozzarella. Sprinkle each tomato slice with a small pinch of coarse or flaked sea salt and freshly ground black pepper. Drizzle with the Balsamic Reduction and top each stack with a basil leaf. Carefully transfer the stacks to a serving platter or individual plates and serve.