Bring a large pot of water and 1 teaspoon of salt to a boil over medium-high heat. Add the pasta and reduce the heat to medium low. Continue to cook following the package directions for al dente pasta. Drain and set aside.
Preheat the oven to 350 F. Lightly grease a 2 1/2-quart casserole dish.
Heat the 4 tablespoons of butter in a large saucepan over medium heat. Add the onion, celery, garlic, and ham and cook, stirring, until the onion is translucent. Add the flour; continue to cook, stirring, for 2 minutes.
Gradually pour the milk into the saucepan while stirring constantly; add 1 teaspoon of kosher salt, the thyme, and pepper. Continue to cook, stirring, until the mixture is thickened. Add the diced chicken, Swiss cheese, and peas. Blend thoroughly and stir in the parsley, if using.
Combine the cooked and drained pasta with the sauce mixture and turn into the prepared casserole dish.
In a small bowl, combine the breadcrumbs with 2 tablespoons of melted butter. Toss to coat the crumbs thoroughly. Scatter the breadcrumbs over the casserole.
Bake the casserole in the preheated oven for about 30 minutes, or until the breadcrumbs are browned and the filling is hot and bubbly around the edges.