Heat olive oil on medium high heat in a large soup pot. Once the oil is hot, add the onions and celery. Fry until the onions are translucent and fragrant
Add the sliced mushrooms to the pot. Cook the mushrooms on medium high heat until they are lightly browned and have released most of their water. Set aside 1 cup of mushrooms, to be added back later.
Add the vegetable stock (or water and salt) and potato cubes to the pot. Stir and bring to a boil. Continue to simmer uncovered on medium-high heat for about 15-20 minutes to allow the potato to cook and some of the liquid to reduce.
Add 1/2 of the can of coconut milk and simmer for another 5-10 minutes. Remove from heat.
Use an immersion blender to puree the soup until smooth, or work in batches with a standing blender then return to pot. Add the additional 1/2 can of coconut milk to the soup. If the soup is too thick for you, add some more water or stock to thin the soup to your desired level. Stir in the reserved cooked mushrooms.
Add salt and pepper to adjust the flavor.
Serve hot with some gluten-free bread or crackers.