In a small bowl, combine 1 tablespoon of mayonnaise with 1 tablespoon of barbecue sauce. Mix them well and then set the bowl aside.

Place a large skillet over medium heat to warm up. Add the brisket slices to the skillet, heating them for about 1 to 2 minutes on each side or until they're thoroughly heated through.

Take your sourdough bread slices and spread the prepared mayo-bbq sauce mixture on the inside of each slice.

On one slice of bread, lay the warmed brisket slices. Place the cheddar cheese slices on top of the brisket, then close the sandwich with the other slice of bread, sauce side down.

Add a small amount of butter to the skillet (now set at a medium-low heat). Once the butter has melted, place your sandwich in the skillet.

Toast the sandwich for about 1 to 2 minutes on each side. You're aiming for a golden-brown crust on the bread and a lovely melt to the cheese.

Once the sandwich is perfectly toasted, remove it from the skillet. Slice it in half and serve immediately.