Preheat the oven to 400°F (200°C). Spread the pumpkin or squash cubes evenly on a baking sheet, toss with 1 tablespoon of olive oil, and roast until tender and caramelized around the edges, about 25-30 minutes.
Meanwhile, heat a tablespoon of olive oil in a large pot over medium heat. Add chopped onion and sauté until soft and translucent, about 5 minutes. The onions should emit a gentle sizzle and become fragrant.
Add minced garlic, ground cinnamon, and chopped sage to the onions. Stir frequently as the spices toast and release their aroma, which should become fragrant within a minute.
Peel the roasted pumpkin or squash and transfer it into the pot. Use a spoon to break it apart slightly as it warms, mixing with the aromatic onion and spice mixture.
Pour in the vegetable broth and bring the mixture to a gentle simmer. Let it cook for about 10 minutes to allow flavors to meld and pumpkin to soften further.
Use an immersion blender or transfer the soup in batches to a blender to blend until smooth and creamy. Be careful when blending hot liquids and pulse until the soup reaches a silky texture.
Stir in the coconut milk to add richness and creaminess. Taste and season with salt and pepper as desired, adjusting to achieve a balanced flavor.
Heat the soup gently if needed, just until it’s hot and steaming, then ladle into bowls. The final soup should be thick, smooth, and warm with a slight sheen from the coconut milk.