Prep. If you are using raw corned beef, you must follow the instructions above. If you have bought corned beef at the deli counter it has already been cooked so move to the next step. If you are using pastrami, it has already been cooked. It is better warm, so throw it in the microwave or steam it.
Dressing. Make the dressing by combining the BBQ sauce and mayo in a bowl or coffee cup. Some folks like to add a teaspoon of sweet pickle relish. If that's what you like, go for it.
Squeeze the sauerkraut in your fist to drain as much of the liquid as possible. Spread it on a paper towel until you are ready to assemble the sandwich.
Fire up. Preheat the grill in a 2-zone setup. Place a griddle or frying pan with an oven safe handle on the hot side of the grill and close the lid. Prep again. On the insides of the bread spread the dressing. Slice the meat if necessary, and on one side layer the meat, then the kraut, and then the cheese. Now cover the pile with the other slice of bread.
Cook. Paint a thin layer of melted butter on one side of each slice of bread with a basting brush. Make sure the edges are buttered so they don't burn. Put the sandwich on the hot griddle or pan. If you wish, you can grill it right on the grill grates, but you won't get all over browning. Press it down lightly with a spatula and close the lid, but don't go away. In about two minutes peek at the bottom. Get the bread golden brown or as dark as you like it, but don't burn it. Flip and repeat.
Serve. Slice in half on an angle and serve with chips and a beer.