Pound chicken breasts between sheets of waxed paper to thickness of 1/4 inch. Arrange chicken breasts shiny side down. Cover each with 1 prosciutto slice. Set 1 Bel Paese cheese oblong in center of each. Place 2 pieces of asparagus beside cheese. Sprinkle with about 3 tablespoons Parmesan mixture, then parsley. Roll up tightly.
Preheat oven to 350 degrees. Heat thin layer of oil in heavy large skillet over medium heat. Dredge chicken rolls in flour, shaking off excess. Arrange seam side down in skillet and brown on both sides. Transfer to baking sheet. Pour oil over. Do not wash skillet. Bake chicken until tender, about 15 minutes.
Meanwhile, set skillet over high heat. Add mushrooms and Marsala. Tilt pan, heat wine and ignite. When flames subside, boil until liquid is reduced by half. Add cream to skillet and boil until reduced to saucelike consistency. Season with salt and pepper.
To serve, set 2 chicken rolls on each plate. Spoon Marsala sauce over.
