In a food processor, pulse 1/2 cup walnuts until finely chopped. Add 2 cups basil and garlic, and pulse while slowly adding 1/2 cup oil, scraping down sides as needed until smooth, about 1 minute. Add parmesan; season with salt and black pepper; process until pesto is well combined. Heat oven to 400 degrees. Brush eggplant slices with remaining 1 1/2 tablespoons oil and sprinkle with sea salt; roast on a baking sheet, turning once, until golden and tender, 20 minutes. Top each with 1 tablespoon pesto. Alternately layer 2 eggplant slices, 2 tomato slices and 1 slice mozzarella. (Refrigerate any remaining pesto for another use.) Divide balsamic vinegar, remaining 2 tablespoons walnuts and basil leaves among stacks.