Season chicken with salt and pepper and dredge in flour, shaking off excess.
Heat 2 tbsp oil or butter in a skillet over medium-high. Brown chicken 3–4 minutes per side; transfer to a plate.
Add remaining oil, sauté mushrooms until golden, about 5 minutes.
Pour in Marsala, scrape browned bits, reduce slightly, then add chicken stock and simmer 3–4 minutes.
Return chicken to pan and simmer until cooked through, 4–5 minutes; stir in 2 tbsp butter and parsley.
Meanwhile cook egg noodles per package, drain, toss with a tablespoon of butter and salt.
Serve chicken and sauce over buttered noodles.