Preheat your oven to 200°C (400°F) and line a baking sheet with parchment paper.
Peel and chop the carrots into evenly sized 2-inch pieces, then toss them with 2 tablespoons of olive oil and a pinch of salt. Spread them out in a single layer on the prepared baking sheet.
Roast the carrots in the oven for about 25-30 minutes, until they are golden and caramelized around the edges, stirring halfway through to ensure even roasting.
While the carrots roast, peel and finely grate the fresh ginger, setting it aside for later.
In a large pot over medium heat, add a splash of oil and sauté the grated ginger for about 1-2 minutes until fragrant, the kitchen filling with a warm, spicy aroma.
Add the vegetable stock to the pot and bring it to a gentle simmer. Once simmering, carefully add the roasted carrots and cook for an additional 10 minutes to allow the flavors to meld.
Use an immersion blender or transfer the soup in batches to a blender, then blend until smooth and velvety, about 1-2 minutes. Be cautious with hot liquids—blend slowly and vent the lid if necessary.
Stir in the coconut milk for added creaminess, then season with salt and pepper to taste. Add a squeeze of fresh lemon juice to brighten the flavor.
Warm the soup gently over low heat if needed, then ladle into bowls. Garnish with extra herbs or a drizzle of coconut milk if desired, and serve hot.