Heat a large pot over medium heat and add a splash of oil. Once shimmering, add the diced onion and cook until translucent, about 5 minutes, until it begins to smell sweet and looks glassy.
Add the chopped carrots and grated ginger to the pot. Stir well and cook for another 3 minutes, until fragrant and slightly softened, filling your kitchen with a warm, spicy aroma.
Pour in the vegetable broth, bringing the mixture to a gentle simmer. Cover partially and cook for about 20 minutes, or until the carrots are very tender and easy to pierce with a fork.
Remove the pot from heat. Use an immersion blender directly in the pot, or carefully transfer the soup in batches to a blender. Puree until completely smooth and velvety, about 1-2 minutes.
Return the blended soup to the stove over low heat. Stir in the coconut milk, and warm gently for 5 minutes, tasting and adjusting salt as needed. Add a splash of lemon juice for brightness, if desired.
Once heated through and seasoned to your liking, ladle the soup into bowls. Garnish with a drizzle of coconut milk or fresh herbs if you like, and serve hot for a comforting, bright bowl.