Heat the oil in a large pot over medium-high heat. When hot, add the celery, carrots, onion, and garlic. Sauté the veggies, until they soften and begin to brown. Add the potatoes and veggie broth. Cover and simmer for about 15-20 minutes, until a fork can easily pierce all the way through the veggies.
Use an immersion blender straight in the pot. Blend until it is perfectly smooth. If you don't have an immersion blender, you can carefully scoop some soup into a standing blender, and blend in very small batches. Remember to not fill your blender up too high or you will have a hot soup explosion! I like my soup creamy and silky, but if you prefer some veggie chunks in yours remove some of the soup, blend, and then mix the two back together again.
Once blended, stir in the coconut milk. Salt to taste. Serve hot with optional toppings of choice.