Peel and chop the carrots into uniform pieces, setting them aside for cooking.
Heat the large pot over medium heat and add the olive oil. Once shimmering, add the diced onion and cook for about 5-7 minutes, stirring occasionally until translucent and fragrant.
Grate the fresh ginger directly into the pot, stirring well to release its spicy aroma. Cook for another 2-3 minutes until fragrant, taking care not to burn it.
Add the chopped carrots to the pot and stir to coat with the onion and ginger mixture.
Pour in the vegetable broth and bring the mixture to a gentle simmer. Cover and cook for about 20 minutes, or until the carrots are tender and easily mashable.
Use an immersion blender directly in the pot or transfer the soup to a blender in batches. Blend until the mixture is completely smooth and velvety.
Stir in the coconut milk and heat gently for another 2-3 minutes. Add lemon juice and season with salt and pepper, tasting and adjusting as needed.
Remove from heat and let the soup sit for a few minutes to settle the flavors. Then, ladle into bowls and drizzle with a little olive oil or garnish with herbs if desired.