Preheat oven to 375 degrees. In a large pot boil the pasta according to package directions and drain and rinse. In a medium skillet over medium high heat add the olive oil, onion, and celery. Sauté for 2-3 minutes until almost tender. Add in the mushrooms and continue to sauté until tender. Add to a large bowl.
Add the butter to the skillet and whisk the flour until golden. Slowly whisk in the chicken broth and milk. Let simmer until thickened.
In the large bowl add the pasta, tuna, peas, and cheese. Mix together. Spread evenly in a 9x13 inch casserole dish. In a small bowl combine parmesan, breadcrumbs, and butter. Sprinkle on top of casserole.
Bake for 25-30 minutes or until bubble and golden brown on top.