This is the Classic Reuben. Absolutely traditional, just how they should be made.
Preheat a large skillet or griddle on medium heat.
Optional: to make certain your corned beef is heated through with the cheese hot and melty and the sandwich perfectly browned, Add a corned beef and sauerkraut each in a separate pile on the skillet. Add a tablespoon or two of the juices the corned beef was cooked in, or a little water. Place a lid on the skillet and allow the corned beef and sauerkraut to steam for a minute or two. Remove the lid, and when the moisture has evaporated,, remove to a plate. Wipe skillet clean.
In the meantime, lightly butter one side of the bread slices and place four in the pan or on a griddle, buttered side down. (take out two slices of bread at a time, and open them like a book and they’ll line up correctly when the sandwich is finished.)
Top each piece of bread with a slice of cheese, a schmear of thousand island, 1/4 of the sliced corned beef and sauerkraut. Top all that with a bit more thousand island and another slice of cheese. Top with the last slice of bread, butter side out. Grill slowly (so they will warm through) until golden brown and toasted, several minutes per side, turning once.
When serving the corned beef, turn it over so the “top” is on the bottom of the plate. It will not be quite as hot as the bottom so it won’t steam on the plate as much, staying crispier.