Eggplant, Tomato and Pesto Stack

1/3 cup plus 2 tablespoons chopped walnuts, divided
2 cups fresh basil leaves, plus more for garnish
3 medium garlic cloves
1/2 cup plus 1 1/2 tablespoons extra-virgin olive oil, divided
1/2 cup grated Parmesan
1 large eggplant, cut into 8 1/2-inch rounds
1 teaspoon sea salt
2 large heirloom tomatoes, cut into 4 slices each
4 slices (4 ounces) fresh mozzarella
1 tablespoon balsamic vinegar
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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°F. Brush eggplant slices with remaining 1 1/2 tablespoons oil and sprinkle with sea salt; roast on a baking sheet, turning once, until tender and golden, 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.