Preheat your oven to 350 degrees. Prepare a 3 quart baking dish by spraying it with cooking spray and setting aside.
Melt the 4 TBSPs butter over medium heat. Once fully melted, add the flour and whisk it in until it is completely combined. Cook until it is just light brown. Add the milk a little bit at a time, starting wit about a tablespoon. Whisk it in until fully combined and then add just another small bit, whisking that until combined. Continue until it is fully combined and all the milk is used.
Reduce the heat, and stir in the cheddar cheese until fully melted into the sauce. Then add in the bbq sauce and the chicken.
Stir in the noodles. You can then serve it as is or you can bake it.
If you bake it, mix together the bread crumbs and melted butter. Pour the macaroni and cheese into the baking dish and then top with the bread crumb mixture and bake for 25 minutes.