Preheat oven to 375. Melt butter in saucepan over medium heat. Saute mushrooms and onions until just tender, about 5 minutes. Stir in flour and cook for 1 minute. Remove from heat and whisk in milk. Return pan to heat and cook, stirring, until it thickens and almost reaches a boil. Remove from heat and stir in cheese; stir until melted.
Drain tuna and break into flakes. Put in large bowl and add sauce, cooked noodles, parsley. Stir together and pour into greased baking dish. Sprinkle top with breadcrumbs. Bake at 375 until browned on top, about 30 minutes.