Preheat your oven to 400°F (200°C) and spread the cubed butternut squash on a baking sheet. Drizzle with 1 tablespoon of olive oil and toss to coat evenly. Roast for about 25-30 minutes until the edges are golden and the squash is tender.
While the squash roasts, heat the remaining olive oil in a large pot over medium heat. Add the chopped onion and sauté for 5-7 minutes until soft and translucent, filling your kitchen with a sweet onion aroma.
Add the sliced ginger to the onions and cook for another 2-3 minutes, stirring often, until fragrant and slightly softened.
Remove the roasted squash from the oven and add it to the pot. Pour in the vegetable broth and bring the mixture to a gentle simmer. Let it cook for about 10 minutes to allow the flavors to meld.
Use an immersion blender to carefully puree the soup directly in the pot until smooth. Alternatively, transfer the soup in batches to a blender and blend until silky, then return it to the pot.
Stir in the coconut milk if using, and season with salt and pepper to taste. Simmer for another 5 minutes, letting the soup thicken slightly and become richly flavored.
Check the seasoning and adjust with more salt or pepper as desired. The soup should be creamy, smooth, and steaming hot.
Ladle the hot butternut squash and ginger soup into bowls, garnish with a extra drizzle of olive oil or a sprinkle of herbs if desired, and serve immediately.