Place noodles in a large skillet. Pour broth over the noodles. Layer chicken, then broccoli over the noodles.
Whisk milk, mayonnaise, flour, dry mustard, garlic powder, salt and pepper in a medium bowl. Pour over the broccoli.
Bring to a simmer over medium-high heat. Reduce heat to maintain a simmer, cover and cook, stirring once or twice, until the noodles and chicken are cooked through, 15 to 18 minutes.
Meanwhile, position rack in upper third of oven; preheat broiler.
When the casserole is done, sprinkle cheese on top and broil until lightly browned, about 3 minutes.
