Slice the eggplant into 1/2-3/4-inch thick rounds.
Lightly season both sides with kosher salt.
Arrange the slices in a vacuum bag in a single layer.
Drizzle the balsamic vinegar evenly over the eggplant.
Vacuum seal using a light compression (approximately 35-45 seconds in a chamber vacuum). The eggplant should compress slightly while retaining its shape.
Sous vide at 194°F (90°C) for 45 minutes.
Immediately chill the bag in an ice bath until cold.
Spoon a layer of marinated tomatoes onto a serving plate.
Add one slice of sous vide eggplant.
Top with a slice of fresh mozzarella.
Repeat with another layer of tomatoes, eggplant, and mozzarella.
Finish with additional tomatoes if desired.
Garnish with fresh basil (or a sprinkle of dried basil).
Drizzle with extra virgin olive oil and a small amount of aged balsamic vinegar.
Season with salt and freshly ground black pepper.
Serve chilled or at cool room temperature as an appetizer or light salad.
