In a large saucepot over medium heat add oil to warm. Add onion and celery and sweat until onions are translucent, about 5 minutes.
Add garlic and sauté; one minute more.
Increase heat to medium high and add mushrooms, sautéing until tender and any liquid has evaporated, about 6 minutes.
Add white wine and bring to a simmer, then add chicken stock, thyme and potato and season lightly.
Simmer soup, loosely covered, over medium heat until potatoes are tender, about 20 minutes.
Purée soup in a blender or using an immersion blender until smooth. Stir in cream, season to taste then cool to room temperature before covering with puff pastry (or prepare a day ahead and chill).
Preheat oven to 400°F.
Place 4 ovenproof soup cups (not bowls that have a lip) on a baking tray and ladle cool soup into them. Cut squares (or circles) of puff pastry that are just under an inch wider than the mouth of each soup bowl.
Brush eggwash onto the top outside edge of each soup cup and place puff pastry over the top, pressing gently but taking care not to tear or puncture the pastry. Sprinkle with coarse sea salt.
Bake soup for about 18 minutes. By the time the pastry is a rich golden brown, it will have created a dome (raised by the steam of the soup) and the soup will be hot within. Lift bowls carefully onto saucers or plates and serve immediately.
Tip: If you like truffle oil, add a drop or 2 to the cool soup before you cover it with the pastry. Once you crack into the dome the fragrance will be released.