In a large pan, sauté mushrooms with 2 tablespoons of butter and 2 teaspoons of kosher salt on medium-high heat. Making sure the mushrooms are nicely browned. Cook for about 7-10 minutes.
While the mushrooms sauté, Cook the potatoes in a heavy bottom pot with olive oil and 2 tablespoons of butter. Cook uncovered on medium heat for 10 minutes. Stir often.
After 10 minutes, add 2 more tablespoons of butter and 3 tablespoons of olive oil, onion, garlic, celery and carrots to the same pot as the potatoes. Sauté together for an additional 5 minutes on medium heat. Add 1 tablespoon of salt and seasonings. Mix to combine.
Add chicken stock, mushrooms, bay leaves and thyme to the pot. Adjust salt if needed. Bring to a boil, turn down heat to low and let it simmer for 10 minutes, uncovered.
Add cornstarch and 2 tablespoons of the heavy cream in a small bowl, whisk to create a slurry. Add to the rest of the cream and then add to the pot of soup. Mix well to combine. Cook for an additional 5 minutes for the soup to thicken. Turn off the heat, remove bay leaves and thyme stems.
Add to a bowl, top with fresh dill and serve with crusty bread.