Position oven rack 6 inches from heat source; preheat broiler. Bring a large saucepan of water to a boil over high heat. Add pasta; cook, stirring occasionally, until al dente, about 8 minutes. Reserve 1 ¼ cups of the cooking water; drain the pasta.
Melt butter in a large broiler-safe skillet over medium-high heat. Add onion; cook, stirring occasionally, until softened, 2 to 3 minutes. Add garlic; cook, stirring constantly, until fragrant, about 1 minute. Add broccoli and broth; cover and cook, undisturbed, until the broccoli is tender and bright green, 3 to 4 minutes.
Stir in cream cheese, milk, the reserved cooking water, Italian seasoning, onion powder, garlic powder, pepper and salt. Cook, stirring often, until a creamy sauce forms, about 2 minutes. Add 1 cup cheese; cook, stirring constantly, until melted, about 1 minute. Add the pasta and chicken; cook, stirring frequently, until heated through. Remove from heat. Sprinkle with the remaining ½ cup cheese.
Broil until the cheese is bubbling and browned, 2 to 3 minutes. Top with Parmesan and parsley. Additional reporting by Carrie Myers, M.S. and Linda Frahm
