Melt butter over medium heat in a large pot. Add shallots, garlic, and sliced mushrooms. Sauté for 10-12 minutes to soften and caramelize mushrooms. Reserve a couple scoops of mixture for topping.
Gradually stir the flour into the sautéed vegetables. Cook 1 minute longer. Stir in broth and bring to a low boil. Add thyme, bay leaf, and Takumi sauce and season with salt and pepper. Reduce heat to medium-low and simmer for 10 minutes.
Discard bay leaf. Ladle soup into a blender and blend until smooth. Return to pot over medium heat and stir in heavy cream. Heat soup through.
Serve hot garnished with extra thyme and reserved mushrooms.
