Preheat oven to 350°F.
Cut butternut squash in half lengthwise, and place halves in a baking dish, cut sides down.
Add approximately 1 inch of water, and cover with foil.
Bake for 1 hour. Allow squash to cool for 15 minutes. Remove and discard seeds.
Scrape out flesh, and purée.
Heat olive oil in a large stock pot over medium heat. Add onion, and sauté for 5 minutes.
Add peppers, and sauté for another 2 minutes.
Add sugar, and stir well.
Add chicken broth and puréed squash, stirring to thoroughly combine.
In a large nonstick pan over medium heat, cook sausage until browned.
Transfer sausage to a paper towel-lined plate, and blot to remove excess grease.
Add sausage to soup.
When soup is heated through, add warmed milk, and stir well.
Season with salt and pepper, if needed