In a dutch oven (or soup pot) over medium heat, add the olive oil, potatoes, onion, carrot, celery, and garlic. Saute for about 5 minutes.
Add the flour and thyme, continue to saute for about a minute then add the dry white wine, broth, and corn kernels. Bring to a simmer, cover, and turn the heat down to medium-low. Allow to cook for 30 minutes.
Transfer half the soup to a blender, and blend until smooth. Then trasnsfer the pureed soup back to the pot. Add the maple syrup, nutritional yeast, liquid smoke, and coconut milk. Stir. Add salt and pepper to taste. Serve hot.
To save: let the soup cool to room temperature, transfer to an airtight container and save in the fridge for about 5 days.