Chop onions, carrots, and celery and add to the pot. Cook for about 5 minutes and then add in the garlic. Let it all cook for another 5–10 minutes while you peel and chop the potatoes.
Toss in the chopped potatoes and immediately add the vegetable broth. Stir in the desired seasonings and cover. Let cook for 35 minutes (or more if not softened enough).
When softened, mash the potatoes and veggies with a potato masher.
Open and stir your canned coconut milk. Pour half of the can into the soup and stir. Keep adding more coconut milk until your soup is soft and creamy.
Optional: If you want a smoother soup, use a hand blender to blend any of the remaining vegetables.