Peel eggplant (unless yours has a very thin skin).
Slice into 1/2-inch rounds. You will need two large or four small rounds per stack.
Brush eggplant with olive oil and season with salt and pepper. Grill the eggplant rounds over medium-high on barbecue or in grill pan on stove until tender (about 10 minutes) turning once. Allow to cool completely.
Slice each tomato into four rounds.
Alternate tomato and eggplant slices, beginning and ending with a tomato slice. If the eggplant slices are too small, just use two for one layer.
Sprinkle each completed stack with a teaspoon of olive oil and two teaspoons of balsamic vinegar.
Season each stack with a pinch of kosher salt and a turn of freshly ground pepper.
Garnish with feta and fresh basil.
Refrigerate until ready to serve.
Stacks can be prepared as much as a day ahead of time. Do the final prep (olive oil, feta and basil) right before serving.
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