Preheat oven to 400.
In a 4qt saucepan, cook the pasta in 2-3 qts of salted water.
Just before the pasta is done, add in the broccoli to quickly blanch.
Strain both and set aside.
In a dutch oven or large skillet, melt butter over medium heat.
Sauté onion in butter until translucent.
Add in garlic and mushrooms and cook until tender.
Mix in flour and broth. Stir until no clumps remain.
Add milk and allow mixture to simmer for 2-3 minutes. Turn down the heat if it begins to boil.
Season with ground mustard, salt, and pepper.
Slowly mix in cheddar.
Once mixture has thickened, turn off the heat.
Combine mixture with cooked pasta, broccoli, and chicken.
Bake for 15 minutes uncovered.
Sprinkle with shredded cheese and bake for 5-10 additional minutes, until cheese is melted but not burned.
Portion or serve.