Preheat oven to 375° F. Butter a large pie pan or medium baking dish and set aside.
Cook noodles in lightly salted water for 8-10 minutes or until al dente. Drain.
Saute the onion, celery, and garlic in 2 T butter until tender. Add mushrooms and saute until most of the liquid has evaporated.
Melt 4 T butter in a large saucepan and whisk in the flour until smooth. Gradually whisk in the milk and cook until sauce is smooth and thickened. Season with salt and paprika, taste and adjust accordingly. Stir in the tuna, peas, sauted vegetables, and pasta. Pour into the baking dish and top with the grated cheese.
Bake 25-30 minutes in the preheated oven, or unitl the cheese is melted and lightly browned on top.