Preheat oven to 375 degrees F . Line a rimmed baking sheet with heavy duty foil.
Place the squash halves cut-side down on the foil-lined baking sheet. Bake for 45 to 50 minutes or until tender all the way through when pierced with a fork or sharp knife. Remove from the oven and allow to cool. When cool enough to handle, remove and discard the skin, using a sharp knife, if necessary. Alternately, you can use a spoon to scoop the flesh out of the skin. You should have about 3 cups of roasted squash.
In a large saucepan or Dutch oven with a lid, heat the 2 tablespoons oil over LOW heat. Add the onion and carrot and cook, until the onion is translucent and the carrot is fork tender, about 10 to 15 minutes. Add the roasted squash, garlic, chicken or vegetable broth, brown sugar, and curry powder and increase the heat under the pot as needed to bring the mixture to a boil. Reduce the heat to LOW, cover the pot, and cook for 10 minutes.
Remove the pot from the heat and use an immersion blender to purée the soup until creamy and smooth. If you don't have an immersion blender, cool the soup for about 5 minutes. Working in batches, purée the soup in a blender or food processor. Transfer the purée to a clean pan as you work.
If you would like to thin the consistency, add additional broth. Season the soup with cayenne pepper and salt, to taste, and simmer a few minutes over MEDIUM heat to enhance the flavors. Garnish with fresh thyme leaves, if desired.
Ladle the soup into bowls and serve with croutons.