Preheat the oven to 375 degrees F (190 degrees C). Butter a medium baking dish with 1 tablespoon butter.

Fill a large pot with lightly salted water and bring to a rapid boil. Cook egg noodles at a boil until tender yet firm to the bite, 7 to 9 minutes. Drain and set aside.

Melt 1 tablespoon butter in a skillet over medium-low heat. Stir in onion, celery, and garlic; cook and stir until tender, about 5 minutes. Increase heat to medium-high and mix in mushrooms. Continue to cook and stir until most of the liquid has evaporated, about 5 more minutes. Remove from heat and set aside.

Melt 4 tablespoons butter in a medium saucepan; whisk in flour until smooth. Gradually whisk in milk and cook until sauce is smooth and slightly thickened, about 5 minutes. Season with salt and pepper. Stir in tuna, peas, mushroom mixture, and cooked noodles. Transfer to the prepared baking dish.

Place remaining 2 tablespoons butter in a microwave-safe bowl; cook in the microwave until melted, about 10 seconds. Mix in bread crumbs until combined and sprinkle over casserole. Top with Cheddar cheese.

Bake in the preheated oven until bubbly and lightly browned, about 25 minutes.