Preheat oven to 400°F. Cut zucchini in half lengthwise. Using an ice cream scoop, scoop out insides, leaving a 1/2-inch edge around the border. Reserve zucchini filling. Do the same for the eggplant and butternut squash until the zucchini fits inside the eggplant and eggplant fits inside the squash. Coarsely chop the reserved vegetable filling, until there are no large pieces.
Over medium heat in a non-stick frying pan, saute 1 tablespoon olive oil with garlic and onion for 5 minutes. Then add the vegetable filling plus 1/4 cup parsley, eggs, bread crumbs, broth and salt to the frying pan. Combine thoroughly in the pan and saute for 10 minutes.
In a small mixing bowl mix 2 tablespoons olive oil with additional minced garlic and thyme. Brush over the insides of the vegetables.
Assemble by spooning the breadcrumb mixture into both cut halves of the butternut squash and sprinkling with hazelnuts. Place the eggplant halves on top of the prepared squash halves, spoon in another layer of the breadcrumb mixture, and another handful of nuts. Repeat with zucchini. Use kitchen twine to secure both stuffed squash halves together. Wrap in foil and bake on a baking sheet for 1.5 to 2 hours until the squash is soft.
In another small bowl combine remaining parsley, 1 tablespoon of olive oil, lemon juice, and salt and pepper to taste.
Serve squash in slices with the herbed olive oil drizzled on top.