Preheat oven to 375°F. Arrange the prosciutto in a single layer on parchment-lined baking sheets and bake 10 minutes until crispy.
Bring a large pot of water to a boil for pasta.
Place the dried mushrooms in a small pot and cover with stock. Bring to boil then reduce heat to a simmer to reconstitute mushrooms.
Heat a large skillet over medium-high to high heat with EVOO, 2 turns of the pan. Melt butter into oil then add fresh mushrooms and brown until tender and deeply fragrant. Add shallots, garlic and thyme, and season with salt and pepper. Turn heat back a bit and cook to soften 2-3 minutes. Remove the porcini from the stock and chop. Add them to the sautéed mushrooms then deglaze the mushrooms with Marsala. Add the porcini stock to pan, leaving behind any grit that has settled at the bottom of the pot, stir in cream and parsley, and reduce heat to a low simmer.
Salt pasta water and cook pasta to al dente. Reserve 1/2 to 3/4 cup starchy cooking liquid then drain pasta. Toss pasta with sauce and a splash of cooking water. Add in cheese slowly, use more cooking water to marry the sauce to pasta if necessary. Serve with more cheese at the table to pass.