Preheat your oven to 400°F (200°C). Spread the chopped pumpkin evenly on a baking sheet, drizzling with olive oil. Roast for about 25-30 minutes until the pumpkin is tender and slightly caramelized around the edges.
Once roasted, transfer the pumpkin to a blender. Add the minced garlic, grated ginger, and smoked paprika to the blender.
Pour in one cup of vegetable broth and blend until smooth and velvety, stopping to scrape down the sides as needed.
Pour the mixture into a pot and add the remaining vegetable broth. Bring to a gentle simmer while stirring frequently, allowing flavors to meld and the soup to thicken slightly.
Stir in the coconut milk to add creaminess, then season with salt and pepper to taste. Continue simmering for about 5 minutes to incorporate the flavors.
Taste and adjust seasoning as needed; if the soup is too thick, stir in a bit more broth until desired consistency is reached.
Serve the soup hot, garnished with a drizzle of coconut milk or a sprinkle of smoked paprika if desired.