Preheat oven to 375° F.
Put a large pot of water on to boil. Cook broccoli in the boiling water until just tender and bright green, about 3 minutes. Transfer to a large bowl with a slotted spoon.
Add pasta to the boiling water and cook according to package directions. Drain and rinse with cold water. Transfer to the bowl with the broccoli.
Heat butter in a large skillet over medium heat. Add chicken, onion, salt, and pepper. Cook, stirring frequently until the onion has softened and the chicken is no longer pink throughout (~ 6- 8 minutes)
Add flour and mustard. Stir until coated. Add milk and bring to a boil. Cook, stirring until thickened slightly (~ 3-5 minutes)
Transfer to the bowl with the broccoli and pasta. Stir in cheese, ham, and parsley. Transfer the mixture to a 9-by-13-inch baking dish, spreading evenly.
Bake until the casserole is heated throughout and the breadcrumbs are beginning to brown, about 30 minutes (or 50 minutes, if casserole has been frozen).
Preheat broiler to high. Sprinkle top of the casserole with herbed bread. Broil on rack 8 inches from heat until the top is browned (~ 2 to 3 minutes)