Bring a large pot of water to a boil. Cook noodles until el dente (6 to 8 minutes at most). Drain and rinse. Preheat broiler.

Meanwhile, heat oil in a large ovenproof skillet over medium-high heat. Add onion, mushrooms and salt and cook, stirring often, until the onion is softened--about 5 minutes. Add wine and cook until evaporated, 4 to 5 minutes. Sprinkle flour over the vegetables; stir to coat.

Add milk, chicken broth and pepper and bring to a simmer, stirring constantly. Stir in tuna, peas and 1/2 cup Parmesan until evenly incorporated. Then, stir in the noodles (the pan will be very full). Remove from the heat and transfer to a oven-proof casserole dish.

Sprinkle the casserole with breadcrumbs, the remaining 1/2 cup Parmesan and the cheddar cheese. Broil until bubbly and lightly browned on top, 3 to 4 minutes (watch carefully that it doesn't burn on top!).