01 - Preheat the oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
02 - In a large pot of salted boiling water, cook the egg noodles until just al dente. Drain thoroughly and set aside.
03 - In a large skillet over medium heat, melt 2 tablespoons of unsalted butter. Add the diced onion, celery, and minced garlic. Sauté for 3 to 4 minutes, stirring occasionally, until the vegetables are softened.
04 - Sprinkle the all-purpose flour over the cooked vegetables. Cook, stirring constantly, for 1 to 2 minutes until the mixture is fragrant and lightly golden.
05 - Gradually whisk in the whole milk, ensuring no lumps remain. Stir continuously until the mixture is smooth and thickens, about 4 to 5 minutes.
06 - Add dried thyme, dried parsley, salt, and black pepper. Stir in the frozen peas and carrots, frozen corn, and shredded chicken. Cook for 2 minutes, allowing the mixture to heat through.
07 - Remove the skillet from heat. Gently fold in the cooked egg noodles, 1/2 cup of shredded cheddar cheese, and all of the grated parmesan cheese until evenly combined.
08 - Transfer the complete mixture to the prepared baking dish. Evenly sprinkle the remaining cheddar cheese over the surface.
09 - In a small bowl, toss the panko breadcrumbs with the melted butter until well coated. Distribute the breadcrumb mixture evenly over the assembled casserole.
10 - Bake uncovered for 25 to 30 minutes, or until the topping is golden brown and the filling is bubbling.
11 - Allow the dish to stand for 5 minutes before serving to set and cool slightly.