Cook the pasta: Bring a large pot of salted water to a boil and cook the pasta until just al dente. During the final minute of cooking, add the broccoli directly to the pot. Drain both together and set aside.
Prepare the sauce: Warm the butter or oil in a large sauté pan over medium-high heat. Add the onion and cook for about 3 minutes. Stir in the mushrooms and garlic, cooking for another 5 minutes or until the mushrooms soften.
Thicken the mixture: Sprinkle the flour over the vegetables and mix well. Let it cook for 1 minute. Pour in the stock, stirring until the mixture smooths out. Add the milk, Dijon mustard, salt, and pepper. Keep cooking until the sauce begins to simmer. Remove from heat and melt in 1 cup of the cheddar. Adjust seasoning if desired.
Assemble the casserole: In a 9×13-inch baking dish, combine the pasta, broccoli, sauce, and chicken. Mix until evenly coated and spread into a flat layer.
Bake: Bake uncovered for 15 minutes. Remove the dish from the oven, scatter the remaining cheddar over the top, and return it to the oven for 10 more minutes, or until the cheese melts thoroughly.
Serve: Enjoy warm. Fresh herbs or a little extra cracked pepper make great finishing touches.
Notes
Pasta: Any variety works—traditional, whole-wheat, egg-based, gluten-free, or alternative-grain.
Broccoli: You can swap in 1 pound thawed frozen broccoli florets if needed.