Preheat your oven to 200°C (400°F). Line a baking sheet with parchment paper and set aside.
Peel and chop the carrots into roughly 2-inch pieces. Spread them evenly on the prepared baking sheet.
Drizzle the carrots with 1 tablespoon of olive oil and sprinkle with a pinch of salt. Toss gently to coat all pieces evenly.
Roast the carrots in the oven for 25-30 minutes, until deeply golden and fragrant, with a slight caramelization around the edges.
While the carrots roast, peel and finely chop the fresh ginger.
Warm 1 tablespoon of olive oil in a large pot over medium heat. Add the chopped ginger and sauté for about 30 seconds until fragrant, with a spicy, zesty aroma filling the kitchen.
Add the roasted carrots to the pot with the ginger. Pour in the vegetable stock and bring to a gentle simmer.
Let the mixture simmer for about 10 minutes, allowing the flavors to meld and the soup to heat through.
Use an immersion blender or transfer the mixture in batches to a blender. Puree until smooth and velvety, careful to hold the lid tight if blending hot.
Return the soup to the pot if needed, then stir in a squeeze of fresh lemon juice and, if using, swirl in the coconut milk for added creaminess. Taste and adjust seasoning with salt and pepper.
Allow the soup to rest for a couple of minutes, then ladle into bowls. Garnish with a drizzle of olive oil or fresh herbs if desired, and serve hot.