Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.
Season zucchini with sea salt and freshly ground black pepper. Drizzle 2 tablespoons olive oil over the zucchini halves.
Bake zucchini in preheated oven until softened, about 10 minutes. Remove to a platter to cool; cut into 2-inch segments, keeping them together to resemble intact halves.
Season eggplant slices on both sides with salt and pepper; arrange onto the baking sheet.
Bake eggplant for 15 minutes, flip, and continue baking until browned, 15 to 20 minutes more; remove to a cutting board and let cool slightly.
Remove and discard skin from eggplant. Chop eggplant flesh and transfer to a large mixing bowl; add tomatoes and garlic.
Chop 3/4 cup basil leaves; add to eggplant mixture and season with 1 teaspoon salt and 1/2 teaspoon black pepper. Drizzle 3 tablespoons olive oil over the mixture; toss to coat. Spoon the mixture onto the zucchini halves. Drizzle balsamic vinegar and more olive oil over the stuffed zucchini. Tear remaining basil leaves and sprinkle over the zucchinis.
