3 tbsps extra-virgin olive oil
PLACE the vinegar in a small, heavy saucepan and bring to a boil over medium-high heat. Reduce the heat to low and gently simmer until the vinegar reduces to about one-quarter of its original volume, about 20 minutes. Check the consistency: It should be syrupy and coat the back of a spoon. Simmer slightly longer if needed.
STORE the reduction in an airtight, heatproof container in the refrigerator; it will keep indefinitely. When you are ready to use it again, bring it to room temperature. Place the uncovered container in hot water until you can stir the reduction, adding drops of hot water as needed to thin it to your desired consistency.
PREHEAT a grill to medium-high heat. Place the eggplant rounds in a single layer on a rimmed baking sheet, and brush both sides with olive oil.
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 to 5 minutes per side. Transfer the eggplant back to the baking sheet to cool. Sprinkle lightly with fine sea salt.
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.
NOTES: Japanese eggplant and small heirloom varieties are not ideal for this recipe. Select a medium globe or Italian eggplant that is tall and round, but not too portly. Eggplant rounds will shrink some when they cook, so try to buy large tomatoes that are slightly narrower than the widest part of the eggplant. You will want to match rounds of equal size once it is time to stack them.
Roasted eggplant works well here if you don’t want to fire up the grill. Roast the oiled eggplant rounds at 400°F, flipping them halfway through cooking, until they are golden and tender through the middle, about 20 minutes.
Store any leftovers in the fridge and enjoy them cold as is or pressed into panini.