Preheat the oven to 350 degrees F (175 degrees C).

Brush flesh of butternut squash with olive oil and place cut-side down on a baking sheet.

Bake in the preheated oven until skin is wrinkled and flesh is soft, about 40 minutes. Scrape flesh into a bowl with a spoon and set aside.

Melt butter in a large pot over medium heat and cook onion until soft and translucent, about 5 minutes. Add squash flesh, 2 cups hot broth, and ginger. Season with curry powder, cumin, salt, and pepper. Bring soup to a boil, reduce heat, and simmer until flavors are well combined, about 15 minutes.

Purée soup with an immersion blender until smooth. Add more hot broth for a thinner soup. Stir in cream and season to taste with sugar, cider vinegar, cayenne pepper, and more salt.