Prepare the Noodles and Vegetables: Begin by boiling the noodles according to the package directions. As the pasta is cooking, shred the chicken and cut the broccoli florets into bite-sized pieces. Once the pasta is done, drain it and set it aside.
Cook the Broccoli: In a steamer or saucepan, cook the broccoli until it is just done. Aim for a bright green color with a bit of crunch remaining. Once cooked, transfer the broccoli and pasta to a large bowl and set aside.
Make the Béchamel Sauce: In a medium saucepan, melt the butter over medium heat. Add in the flour, whisking continuously to combine it into a smooth paste. Gradually pour in the milk, about a half cup at a time. Allow the mixture to thicken before adding more milk. Season with salt, cracked black pepper, the minced garlic cloves, and a pinch of nutmeg. Continue whisking until the sauce is thickened, then remove from heat.
Combine the Ingredients: Add the shredded chicken to the bowl with the pasta and broccoli. Sprinkle in additional salt and cracked black pepper to taste. Pour the prepared béchamel sauce over the mixture and use a large spoon to stir everything together thoroughly.
Assemble the Casserole: Spray or grease a casserole dish to prevent sticking. Pour the entire contents of the bowl into the prepared casserole dish, spreading it evenly. Top with an even layer of cheese of your choice. In a small saucepan, melt some butter and add bread crumbs, stirring until the bread crumbs are moistened. Sprinkle these bread crumbs evenly across the top of the casserole.
Bake the Casserole: Preheat your oven to 350℉. Bake the casserole for 20 to 25 minutes, or until the bread crumbs are golden and crispy brown, and the cheese is bubbling. Once fully cooked, remove from the oven and let it cool slightly before serving.
