Heat olive oil in a large soup pot over medium heat. Add the onions, celery and garlic. Cook until slightly softened. Add the carrots, potatoes, vegetable broth, thyme and bay leaf. Cover with lid and cook for 15 minutes.
After cooking for 15 minutes, add white mushrooms, and coconut milk. Cook for five minutes, then remove about 2 tablespoons of liquid from the pot and mix together with cornstarch to create a slurry. Add back to the pot along with the peas.