Heat olive oil in a large saucepan over medium heat. Add onions and garlic and saute until translucent, about 4 minutes. Add ginger and saute for another 4 minutes, until softened and fragrant. Add the potatoes and diced carrots and stir well. Add the vegetable broth or water, bring to a boil, then reduce heat and simmer mixture until carrots and potatoes are softened, about 30 minutes.

Remove from heat. Using an immersion blender or regular blender, blend soup until smooth. Stir in coconut milk. Add salt and pepper to taste. Reheat gently on low heat and serve.