Remove stems from mushrooms. Place stems and stock in a medium saucepan over medium-high heat; bring to a boil. Reduce heat to low; simmer for 30 minutes. Strain; set aside.
Place 3 tablespoons butter in a large skillet over medium heat; add shallots, and cook until translucent, 3 to 5 minutes. Add mushrooms, and cook until mushrooms are soft, browned, and all liquid has evaporated. Add Marsala, if using, and cook, stirring with a wooden spoon to loosen any browned bits on bottom of pan. Remove from heat; set aside.
Combine remaining 3 tablespoons butter and flour in a medium saucepan over medium heat; cook, stirring until incorporated and browned, 2 to 3 minutes. Slowly whisk in stock; bring to a boil, whisking until thickened. Stir in reserved mushroom mixture and thyme. Serve hot.