Grease a 12 3/4” x 10 3/8” x 2 1/2” aluminum pan with the 2 Tbsp. butter, and then set aside. Boil macaroni in a generous amount of lightly salted water until just tender, about 8 minutes.
While macaroni cooks, melt the 1/4 cup butter in a pot set over medium heat. Mix in the flour, cook and stir 2 minutes. Whisk in 1/2 cup of the milk. Cook until the mixture becomes quite thick, and then slowly whisk in remaining milk. Bring to a simmer, stirring frequently so it does not scorch on the bottom. Cook one minute to thicken, and then remove from the heat. Mix in the barbecue sauce, Tabasco, Worcestershire and three-quarters of the cheese. Season the sauce with salt and pepper.
When the macaroni is cooked, drain well. Mix it into the sauce, and then spoon into the pan. Top pasta with remaining cheddar cheese and Parmesan cheese. Cover macaroni with foil.
Preheat your barbecue until the temperature in the chamber is 375 degrees F. Turn the heat off on one side of the barbecue; leave the other side on. Set macaroni on unlit side of the barbecue, close the lid and cook 20 minutes. Remove foil and cook 10 to 15 minutes, or until bubbly and delicious.
Note: You can warm the milk to just below a simmer in the microwave.