Preheat oven to 400 degrees F. Lightly oil a baking sheet or coat with nonstick spray.
In a large bowl, combine bread crumbs and lemon zest; set aside.
Season chicken with salt and pepper, to taste. Working one at a time, dredge chicken in flour, dip into eggs, then dredge in bread crumbs mixture, pressing to coat.
Place butternut squash in a single layer onto one side of the prepared baking sheet. Stir in 2 tablespoons olive oil and thyme; season with salt and pepper, to taste.
Place chicken in a single layer in the middle of the prepared baking sheet and coat with nonstick spray. Place into oven and bake until golden brown and crisp, about 18-20 minutes.
Add asparagus onto the opposite side of the prepared baking sheet in a single layer during the last 10-12 minutes of cooking time. Drizzle with remaining 2 tablespoons olive oil and sprinkle with Parmesan.
Serve immediately, garnished with parsley, if desired.