Preheat the oven to 375°F. Coat the interior of a 9 × 13-inch baking dish generously with butter.
Prepare the ingredients before cooking. Dice the onion and celery, finely mince the garlic, chop the mushrooms, drain and flake the tuna, and shred the cheddar cheese.
Bring a large pot of generously salted water to a boil. Add the pasta and cook until just al dente, stopping approximately 1 to 2 minutes before the package’s recommended cooking time because the pasta will continue softening in the oven.
Drain the pasta thoroughly and place it aside.
Melt 2 tablespoons of butter in a large skillet over medium heat. Add the diced onion and celery, then cook for approximately 3 minutes, or until the vegetables begin to soften.
Add the minced garlic and stir for about 30 seconds, cooking only until aromatic. Incorporate the chopped mushrooms and continue cooking for 8 to 10 minutes, stirring periodically, until their released liquid has evaporated and the mushrooms begin to brown.
Distribute the flour evenly over the sautéed vegetables. Stir continuously for approximately 1 minute to remove the raw flour flavor and form the foundation of the sauce.
Gradually add the room-temperature milk and the chicken or vegetable stock, stirring constantly to maintain a smooth consistency.
Cook the sauce over medium heat for 5 to 7 minutes, stirring frequently, until it becomes thick enough to cling to the back of a spoon. Season to taste with kosher salt and freshly ground black pepper.
Combine the melted tablespoon of butter with the breadcrumbs in a small bowl. Stir until the crumbs are evenly moistened, then reserve the mixture for the topping.
Remove the skillet from the heat. Gently fold the cooked pasta and drained tuna into the mushroom sauce until the ingredients are evenly distributed and fully coated.
Transfer the tuna and pasta mixture to the prepared baking dish, spreading it into an even layer.
Scatter the buttered breadcrumbs uniformly over the casserole, then distribute the shredded sharp cheddar cheese across the surface.
Bake for 20 minutes, or until the edges are bubbling and the topping has developed a golden-brown finish.
Allow the casserole to stand for 5 minutes before serving so the filling can settle slightly while remaining hot and creamy.