Preheat oven to 375°F (190°C). Bring a large pot of salted water to a boil. Add penne and cook until al dente, adding the broccoli florets during the last 3 minutes of cooking. Drain well and set aside.

While pasta cooks, heat olive oil in a large skillet over medium-high heat. Season chicken cubes with salt, pepper, and Italian seasoning. Sauté for 5-7 minutes until golden brown and cooked through. Remove from skillet and set aside.

In the same skillet, melt butter over medium heat. Add minced garlic and cook for 30 seconds until fragrant. Slowly whisk in the heavy cream and bring to a simmer. Cook for 3-4 minutes until slightly thickened. Remove from heat and stir in the grated Parmesan, nutmeg, salt, and pepper until smooth.

In a large bowl, combine the cooked pasta, broccoli, chicken, and the Alfredo sauce. Toss gently to coat everything evenly.

Pour the mixture into a 9x13 inch baking dish. Top with the shredded mozzarella cheese. Bake for 20-25 minutes, until the sauce is bubbly and the top is golden brown.

Let the bake rest for 5-10 minutes before serving. This allows the sauce to set slightly. Garnish with fresh parsley if desired.