Preheat the oven to 375°F.

Bring a large pot of salted water to a boil and cook the pasta until just shy of al dente, about 1 minute less than the package directions. During the last 2 minutes of cooking, add the broccoli florets to the pot to blanch them. Drain the pasta and broccoli well.

Meanwhile, melt the butter in a large saucepan over medium heat. Add the garlic and cook for about 30 seconds, until fragrant. Whisk in the flour and cook for 1 minute. Gradually whisk in the milk and heavy cream, stirring constantly, and simmer for 3 to 5 minutes until the sauce has thickened. Season with the salt, black pepper, garlic powder, onion powder, and nutmeg. Remove the saucepan from the heat and stir in 1 cup of the Parmesan cheese until melted and smooth.

In a large mixing bowl, combine the cooked pasta, broccoli, chicken, 1 cup of the mozzarella cheese, ½ cup of the Parmesan cheese, and the Alfredo sauce. Toss until everything is evenly coated, then transfer the mixture to a greased 9×13-inch baking dish. Sprinkle the remaining 1 cup mozzarella and ¼ cup Parmesan evenly over the top.

For a crispy topping, toss the panko breadcrumbs with the melted butter and sprinkle them over the cheese.

Bake uncovered for 25 to 30 minutes, or until the casserole is hot and bubbly and the cheese is golden brown. For extra browning, broil for 1 to 2 minutes just before serving.