Preheat oven to 350°F. Using about 2 tbsp of softened butter, grease a 9 X 13-inch baking pan. Set aside.
On a rimmed sheet pan, toss the squash in olive oil, 1 tbsp of salt and freshly ground black pepper. Transfer to the oven and roast for 35 minutes, or until the squash is tender but not falling apart. Remove the pan from the oven and set aside.
Heat remaining butter in a large skillet over medium heat. Cook onions, leeks and thyme, stirring occasionally until translucent, about 10-12 minutes. Season with salt and set aside.
To make the egg royal, whisk together the eggs, yolks, heavy cream, 1/2 teaspoon of salt and pepper along with the chopped parsley.
In a large bowl, combine diced bread and cooked vegetables.
Add egg royal and coat everything evenly, refrigerate and allow to absorb into mixture for 2 hours minimum.
Bake bread pudding for 30 minutes at 350, then raise oven temperature to 375 and bake 10-15 minutes until golden brown on top.
Remove from oven and allow to rest 15-20 minutes before serving. Enjoy!