Cook pasta in salted water according to package directions. Scoop the pasta into a drainer or bowl and reserve the hot pasta water.
Add the broccoli to the pasta water and cook for about 3 minutes or until desired tenderness. Drain and set aside.
While pasta is cooking, make the cheese sauce. Over medium-high heat, melt butter in a large sauce pan and whisk in the flour. Cook while whisking for about 2 minutes.
Add milk and whisk continuously to avoid any clumps. Cook until mixture thickens and begins to bubble, stirring often, about 5 minutes.
Stir in the mustard and season with kosher salt and freshly ground black pepper.
Remove from the heat and stir in the cheeses. Add the chicken, the whole wheat pasta, and the broccoli and stir to combine. Season with more salt and pepper to taste and garnish with shredded parmesan cheese. Serve hot.
