Preheat your oven to 200°C (400°F). Line a baking sheet with parchment paper.
Peel, seed, and cut the butternut squash into 2.5cm (1-inch) cubes, and peel the carrots, chopping them into similar-sized pieces.
Toss the squash and carrots with olive oil, grated ginger, salt, and pepper until evenly coated. Spread them out in a single layer on the prepared baking sheet.
Roast the vegetables for 30-40 minutes, flipping halfway, until they are golden around the edges and smell sweet and earthy.
Transfer the roasted vegetables to a large pot and pour in the vegetable broth, just enough to cover the vegetables comfortably.
Bring the mixture to a gentle simmer over medium heat, cooking for about 10 minutes to let flavors meld. Taste and adjust seasoning if needed.
Use an immersion blender to purée the soup directly in the pot until smooth and velvety, or carefully transfer in batches to a blender and blend until silky.
Return the puréed soup to low heat, stir in the coconut milk if using, and simmer for another 5 minutes to warm through and enrich the flavor.
Taste the soup and adjust the seasoning with more salt or pepper as needed. It should be bright, smooth, and inviting.
Serve hot, garnished with a drizzle of extra virgin olive oil or a sprinkle of fresh herbs if desired. Enjoy the cozy, smoky sweetness in every spoonful!