Heat olive oil in a large pot over medium heat. Add chopped onions and cook until translucent, about 5 minutes.
Stir in minced garlic and grated ginger, cooking until fragrant, about 1 minute.
Add the carrots and vegetable broth. Bring to a boil, then reduce heat and simmer until carrots are tender, about 20 minutes.
Remove from heat and let it cool slightly. Use an immersion blender to puree the soup until smooth. Alternatively, transfer to a blender in batches.
Return the pureed soup to the pot and stir in the coconut milk. Reheat gently over low heat.
Season the soup with salt and black pepper to taste.
Serve hot, garnished with additional coconut milk or fresh herbs, if desired.