Preheat broiler. Lightly grease a 2-quart square baking dish; set aside. Trim ends off zucchini. Slice zucchini lengthwise into 1/8-inch-thick slices. Place in a single layer on a baking sheet. Brush with 1 teaspoon of the oil. Broil 3 to 4 inches from the heat about 5 minutes or until zucchini is crisp-tender, turning once. Cool. Adjust oven temperature to 375 degrees F.
Meanwhile, in a food processor, combine onions, carrots, and garlic. Cover and process until finely chopped. In a large saucepan, heat the remaining 3 teaspoons oil over medium-high heat. Add onion mixture; cook and stir about 5 minutes or until tender. Add marinara sauce, basil, and pepper. Bring to boiling; reduce heat. Cover and simmer for 10 minutes, stirring occasionally.
To assemble, arrange three of the noodles in the prepared baking dish. Spread with one-third of the sauce. Sprinkle with about 3 tablespoons of the nuts. Top with one-third of the zucchini and one-third of the cheese mixture. Repeat layering noodles, sauce, nuts, zucchini, and cheese mixture, alternating the direction of the zucchini in each layer. Top with the remaining noodles, remaining sauce, remaining nuts, and remaining zucchini.
Cover dish with foil. Bake for 20 minutes. Sprinkle with the remaining cheese mixture. Uncover and bake about 20 minutes more or until heated through. Let stand for 15 minutes before serving. If desired, sprinkle with additional chopped walnuts. Makes 6 servings.