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.