Season the chicken breasts on both sides with salt and pepper. Melt 1 tablespoon of the butter and 1 tablespoon of olive oil in a large skillet. Cook chicken, turning once until browned on both sides and fully cooked (the internal temperature has reached 165 degrees). Transfer to a plate and allow the chicken to cool. Once the chicken has cooled slice it into strips.
Cook pasta according to package directions. Meanwhile, melt 1 tablespoon of butter in a skillet, add garlic, mushrooms, and onions. Cook until the onions are almost tender (about 5 minutes). Add Marsala wine, chicken broth, and heavy cream. Bring to a boil. Reduce heat and simmer until the sauce is thickened. Add cooked chicken slices to the pan.
When the noodles are done the cooking, drain and toss them with 3 tablespoons of butter. Dump noodles into a serving dish. Add the mushroom, chicken, and marsala sauce mixture and ½ cup of parmesan cheese. Season with salt and pepper. Toss until well combined. Serve with parmesan cheese and chopped Italian parsley.