Heat a large pot over medium-high heat. Drizzle in olive oil. Add onion, ginger, and garlic. Cook until the onion starts to turn translucent, 2-3 minutes. Add squash, thyme, and broth and bring to a boil. Stir in cinnamon, nutmeg, pepper, and rosemary. Reduce heat and simmer uncovered stirring occasionally until squash is tender, about 20-30 minutes.
Discard thyme. Using an immersion blender, puree soup until smooth. (May also be added in small batches to a stand blender). Stir in heavy cream and heat through.
Add goat cheese to top of soup. Drizzle soup with small amount of Wild Rosemary olive oil if desired.