In a large pot heat oil at a medium high heat.
Add onion and saute until soft and tender, about 5 minutes.
Add mushrooms until slightly brown, about 5 minutes.
Add carrots, celery, and thyme and saute until celery is tender, about 5 minutes.
Add garlic and saute for about 1 minute.
Add vegetable broth and bring it to a boil.
Add potatoes and reduce to a simmer. Simmer for 12-15 minutes.
Add artichokes, coconut milk, and almond milk (or other non-dairy milk of your choosing) and simmer for an additional 5 minutes.
Season with salt and pepper to taste.