Heat the butter and olive oil in a medium Dutch oven over medium heat. Add the shallots and mushrooms along with the thyme. Cook, stirring occasionally, for 5-7 minutes.
Add the minced garlic and cook, stirring constantly, for 1 minute.
Add the chicken broth and bring to a boil. Reduce the heat to low. Remove half of the mushrooms from the soup and set aside.
Blend the soup with a blender or immersion blender until creamy.
Add the mushroom slices back into the soup along with the milk or cream. Simmer for 10 minutes. Season with freshly cracked pepper and sea salt, to taste.
Serve with additional thyme leaves on top if desired. Enjoy.