Bring a large pot of salted water to a boil. Cook noodles until just tender, 6 to 8 minutes or according to package directions. During the last minute of cooking, add the English peas. Drain and rinse.

Position rack in upper third of oven and preheat broiler on high.

While the water is boiling for the pasta, heat oil in a large ovenproof skillet over high heat. Add onion and mushrooms and cook, stirring occasionally, until they are fragrant, about 5 minutes. Add butter to pan and melt while stirring into onion and mushrooms. Sprinkle flour over the vegetables, stir to coat, and allow to cook until roux is fragrant, 3-4 minutes. Reduce heat to medium and add milk; bring to a simmer, stirring constantly. Stir in tuna and 1/2 cup of the cheese until evenly incorporated. Remove from heat. Then, stir in the noodles (the pan will be very full).

Sprinkle the casserole with the remaining cheese. Broil until bubbly and lightly browned on top, 3 to 4 minutes.