Pre-heat the oven to 350. Grease a 9x13 baking dish or spray with cooking spray. Cook pasta until al dente, drain, and set aside.
I find it easiest and fastest to cook the chicken on the grill while I prepare the next steps. However, you can cook it in a large sauté pan or a large skillet over medium-high heat. Cut the chicken into bite-size pieces and sprinkle the pieces with salt and pepper. Add 1 tablespoon olive oil and 1 tablespoon butter. Cook 6-7 minutes, stirring occasionally, until the chicken is slightly browned and no longer pink. Remove the chicken from the pan and set aside.
In a large saucepan or deep skillet over medium heat, add olive oil and prosciutto. Cook until lightly crisp on the edges, about 5 minutes. Remove the prosciutto to a paper lined plate.
In the same skillet, add the mushrooms and garlic. Cook until mushrooms darken slightly and the juices are released. Remove the mushrooms to the plate with the prosciutto.
In same skillet, melt the butter. Whisk in the flour and cook for 1 minute or until bubbly. Stir in the Marsala and bring to a boil for 1 minute. Add chicken broth and bring to a boil, then whisk in ¼ cup of the parmesan until melted. Remove from heat and add cream and milk. Stir in mushrooms, prosciutto, and chicken.
To the baking dish, add pasta and spoon sauce over the top. Lightly mix the sauce into the dish. Top with reserved ¼ cup of parmesan cheese. Bake uncovered for 20 minutes or until the cheese melts and starts to turn golden. Remove and top with chopped parsley if desired.