Peel the butternut squash, slice in half horizontally and remove the seeds. Dice into even-sized cubes.
Peel and slice the carrots into even-sized pieces. Coarsely chop the onion and garlic.
Heat the olive oil in a medium saucepan. Add the chopped onion, diced carrots, and cubed butternut squash. Season with salt, pepper, cinnamon and brown sugar and sauté for 3 minutes.
Add the chopped garlic and sauté an additional minute.
Pour the broth over the vegetables and bring to a boil.
Boil until tender, about 10 minutes. You should be able to easily pierce the squash and the carrots with a fork.
Transfer the contents to a blender and very carefully blend on the lowest setting until smooth. You may have to work in batches for the liquid to not spill over the top.
Return the soup to the saucepan and stir in the heavy cream or half and half before serving.