Preheat oven to 375°F.
Place squash halves, cut side up, onto a baking sheet and place one tablespoon of butter and sugar into the cavity of each.
Roast squash for about 1 hour or until the flesh has softened.
Allow the squash to cool for 15 minute before scooping the flesh into a bowl. Discard the skin.
Heat oil in saucepan over medium-high heat. Add onions and sauté for 5 minutes.
Add thyme and chives and sauté for an additional 2 minutes. Season with salt and pepper.
Add curry powder, cumin, cinnamon, and squash and stir until just combined.
Pour the broth over the mixture and stir. Simmer soup for 15 minutes. Season with salt and pepper.
Pour mixture into a blender (or use an immersion blender) and puree until smooth.
Pour the soup back into the pan and adjust seasonings. Simmer for 5 minutes, remove from heat. Whisk cream into soup and set aside.
For garnish: Fill a small saucepan with oil and preheat to 350°F. Roll small amounts of goat cheese into a ball and dredge in flour, shaking off any excess. Dip each ball in the egg and roll in the breadcrumbs. Carefully drop each ball of goat cheese into the oil and fry for 15 to 30 seconds (these fry very quickly so keep an eye on them). Drain onto paper towels and lightly season with salt and pepper.
Top each serving of soup with a few goat cheese balls and serve warm.