Heat the oven to 375°F. Bring a large pot of water to a boil. Set a 9x13-inch baking dish nearby.
Cook the egg noodles in the boiling water until 2 minutes shy of package al dente time, 5–7 minutes. Drain and set aside.
Meanwhile, heat the olive oil and 3 tbsp of the butter in a large skillet over medium heat until the butter foams. Add the onion and celery; cook, stirring, until softened, 5–7 minutes.
Add the mushrooms; cook until they release their liquid and the edges are lightly browned, 6–8 minutes. Stir in the garlic and cook until fragrant, 30 seconds.
Add 2 tbsp more butter to the skillet and let it melt. Sprinkle in the flour and cook, stirring constantly, 1–2 minutes to form a blond roux.
Gradually whisk in the chicken broth, then the milk, until smooth. Bring to a simmer and cook until the sauce thickens enough to coat the back of a spoon, 4–6 minutes. Season with the kosher salt and black pepper.
Off the heat, fold in the peas, tuna, and drained noodles until evenly coated. Transfer the mixture to the baking dish and spread in an even layer.
Melt the remaining 2 tbsp butter. In a bowl, toss the panko with the melted butter and parmesan until evenly moistened, then scatter evenly over the casserole.
Bake until bubbling at the edges and the topping is golden brown, 20–25 minutes. Let rest 10 minutes before serving.