Cook the lasagna noodles according to the package directions. Drain and set aside. Preheat the oven to 350°F.
Meanwhile, melt the butter in a large saucepan over medium heat. Add the garlic and cook until fragrant, about 1 minute. Stir in the heavy cream and bring to a gentle simmer.
In a small bowl, whisk together the milk and flour until smooth. Slowly pour the mixture into the saucepan, whisking constantly until the sauce thickens. Stir in the Parmesan cheese until melted and smooth, then remove from the heat.
Spread a thin layer of Alfredo sauce in the bottom of a 9×13-inch baking dish. Add a layer of lasagna noodles, followed by mozzarella cheese, broccoli, shredded chicken, and more Alfredo sauce. Repeat the layers, finishing with noodles, the remaining Alfredo sauce, and the remaining mozzarella.
Bake for 20 minutes, or until the cheese is melted and bubbly. Let the lasagna rest for 10 minutes before slicing and serving.
Notes
Whisk the milk and flour mixture well before adding it to keep the sauce smooth.
Cut the broccoli into small pieces so it cooks evenly.
Blend in provolone or fontina with the mozzarella for extra flavor.
Let the lasagna rest for 10 minutes before slicing.