Prepare Pasta and Broccoli:
Bring a large pot of salted water to boil
Add pasta and cook until almost tender (al dente)
Two minutes before pasta is done, add broccoli to the same pot
Drain pasta and broccoli thoroughly (do not rinse)
Make Cheese Sauce:
Melt butter in a large sauté pan over medium-high heat
Add sliced onions and cook for 3 minutes until translucent
Add minced garlic and cook for 3 minutes, stirring frequently
Sprinkle flour over onion mixture and stir constantly for 1 minute
Slowly add chicken stock while whisking continuously
Stir in milk, Dijon mustard, salt, and pepper
Simmer for about 3 minutes until slightly thickened
Remove from heat and stir in 1 cup of shredded cheddar cheese until smooth
Assemble and Bake:
Preheat oven to 400°F
In a 9x13-inch baking dish, combine pasta, broccoli, chicken, and cheese sauce
Toss to ensure even distribution and spread evenly in dish
Bake uncovered for 15 minutes
Remove from oven and sprinkle remaining 1 cup cheese on top
Return to oven and bake for an additional 10 minutes until cheese is melted and golden
Let rest for 5 minutes before serving