1. Melt the butter in a saucepan. Whisk in the flour and cook for 3 minutes.
2. Whisk in the milk. Simmer for 20 minutes. Add the sherry. Set aside.
3. Preheat the oven to 375 degrees F. Add the broccoli to a well-oiled casserole dish. Top with the chicken. Pour the sauce over the mixture. Sprinkle on the cheese.
4. Bake for 18 to 20 minutes or until lightly browned.