Remove stems from portobello, shiitake, and cremini mushrooms. Place stems and mushroom stock in a medium saucepan over medium-high heat; bring to a boil. Reduce heat to low; simmer for 30 minutes. Strain; set aside.
Finely chop portobello cap, and set aside. Thinly slice shiitake and cremini. Place 3 tablespoons butter in a large saute pan over medium heat; add shallots, and cook until translucent, 3 to 5 minutes. Add chopped and sliced mushrooms, and cook until mushrooms are soft and browned, and all liquid has evaporated. Add Marsala, if using, and cook, stirring to loosen any browned bits on the bottom of the pan. Remove from heat, and set aside.
Place the remaining tablespoon butter and flour in a medium saucepan over medium heat; cook until browned and fully combined, 2 to 3 minutes. Slowly whisk in the enriched stock; bring to a boil, whisking until thickened. Add the reserved mushroom mixture and thyme, and stir to combine. Serve hot.