Preheat your oven to 375 degrees F.

Bring a large pot of salted water to a boil. Cook the egg noodles according to package directions but pull them just before fully done. Drain and rinse with cold water immediately to stop the cooking.

Melt 3 tablespoons of butter in a large skillet over medium heat. Add the chopped onion and celery and cook, stirring occasionally, until soft and translucent, about 4 to 5 minutes.

Sprinkle the flour over the vegetables and stir constantly for 30 seconds. Slowly pour in the chicken broth and milk, stirring as you go to prevent lumps. Add the salt, pepper, and thyme. Cook for 2 to 3 minutes, stirring often, until the sauce thickens enough to coat the back of a spoon.

Remove the skillet from the heat. Stir in the frozen peas and carrots, drained tuna, shredded cheddar, and cooked noodles until evenly combined. Transfer the mixture into a 9x13-inch baking dish and spread it out evenly.

In a small bowl, mix together the panko, Parmesan, and melted butter until the crumbs are evenly coated. Sprinkle the topping over the casserole in an even layer.

Bake uncovered for 15 to 20 minutes, until the casserole is hot and bubbling around the edges and the topping is deep golden brown. Let it rest for 5 minutes before serving. Garnish with chopped fresh parsley if desired.