Preheat oven to 425°F. Toss broccoli with olive oil, Parmesan, garlic powder, salt, and pepper. Spread on a baking sheet and roast 18–22 minutes until edges are golden. Set aside. Reduce oven to 375°F.
Cook penne in salted boiling water until just under al dente (1–2 minutes less than package directions). Drain and set aside.
Season chicken cubes with Italian seasoning, garlic powder, onion powder, salt, and pepper. Heat olive oil in a large skillet over medium-high heat. Cook chicken in a single layer, 3–4 minutes per side, until golden and cooked through (165°F internal). Remove and set aside.
In the same skillet over medium-low heat, melt butter. Add garlic and cook 1–2 minutes until fragrant. Pour in heavy cream and simmer 4–5 minutes until slightly thickened. Remove from heat, whisk in Parmesan until smooth. Season with salt, pepper, and nutmeg.
Grease a 9x13-inch baking dish. Combine cooked penne, chicken, roasted broccoli, and grape tomatoes in a large bowl. Pour Alfredo sauce over everything and toss to coat. Transfer to baking dish. Top with mozzarella and provolone.
Bake at 375°F for 15–20 minutes until cheese is melted and bubbling. Broil 2–3 minutes for a golden top. Rest 5 minutes before serving. Garnish with fresh parsley and extra Parmesan.