Heat 2 tablespoon of olive oil in a large non-stick pan and over medium heat. Add onion and carrot and sauté stirring from time to time until onion is translucent, about 5-7 minutes.
Transfer vegetables to a plate and add mushrooms. Cook stirring occasionally until liquid evaporates and mushrooms start to brown, 5-7 minutes.
Meanwhile, add vegetable stock to a large stockpot and bring it to a boil. Add potatoes, reduce heat to medium-low and cook for 10 minutes.
Add sautéed onion, carrot, ¾ of all mushrooms, 1 tsp of thyme, 1 tsp of salt and ¼ tsp pepper and cook until potatoes are tender, about 5 more minutes.
Add 1 cup of half and half, bring soup to a boil, add 3 cloves of garlic pushed through a garlic press and remove soup from the heat.
Using an immersion or stand blender, puree the soup.
Ladle the soup into bowls, top with the remaining mushrooms and serve with a crusty baguette.
