Heat oven to 400°F. Place butternut squash on a bake sheet in single layer. Spray vegetable oil on top and sprinkle lightly with salt and pepper; toss to coat. Roast until tender, stirring occasionally, about 20 minutes. Transfer to a large bowl to cool.
Melt butter in heavy bottom large skillet over medium heat. Add leeks, celery, and fennel. Cook for 8 minutes. Add sausage. Cook until vegetables are tender and sausage is cooked through, breaking up sausage while cooking, about 10 minutes. Add all herbs; stir and cook 1 minute longer. Add to bowl with butternut squash. DO AHEAD: This portion can be made 1 day ahead. Cool, cover, and chill.
Heat oven to 350°F. Divide bread between 2 rimmed baking sheets. Bake until bread is crusty but not hard, reversing sheets after 5 minutes, 10 to 12 minutes total. Transfer to very large bowl and cool.
Butter 13x9x2-inch baking dish. In a bowl, whisk together salt, pepper and Parmesan cheese. Add chicken stock and eggs; whisk to combine. Pour 1 cup of liquid over bread and vegetable mixture tossing to combine evenly and adding more liquid by ¼ cup as needed if dry. Transfer stuffing to prepared dish.
Bake stuffing uncovered until cooked through and brown and crusty on top, 60 minutes. Let stand 10 minutes.