Preheat oven to 200 degrees. Prepare a rimmed baking sheet with a wire rack.
To assemble the sandwiches:
On a flat surface, lay out 4 slices of bread.
Spread 1 tablespoon of thousand island dressing on each piece. Layer one piece of Swiss cheese, 1/3 cup sauerkraut, 1 more tablespoon dressing, 6 ounces corned beef, one more slice Swiss cheese, and 1 additional tablespoon of dressing.
Top each sandwich with another slice of bread and press each sandwich down gently.
To cook the sandwiches:
Brush the tops of two sandwiches with melted butter. Lay them butter-side down in a large skillet. Place a Dutch oven or large pot onto the tops of the sandwiches and cook over medium-low heat until crisp and golden, about 5 minutes.
Remove the pot and brush the tops with melted butter. Gently flip over sandwiches. Place pot back on top of sandwiches and cook until the bottom side is crisp, about 5 minutes. Transfer the sandwiches to the prepared baking sheet and place in the oven to keep warm. Repeat the process with remaining two sandwiches.
Rye bread: Take your pick; seeded rye, pumpernickel, and marbled rye all work well.
Thousand island dressing: While thousand island is the traditional spread, some recipes call for Russian Dressing. The latter isn't made with pickle relish and can be spicy. Both make excellent Reubens.
Swiss cheese: You'll need 2+ slices of Swiss per sandwich.
Sauerkraut: You can certainly make your own sauerkraut, but store-bought canned fermented cabbage works just as well, too.
Corned beef: Stock up on sliced corned beef at the deli, or you can make your own from scratch.
Yield: One recipe makes 4 sandwiches.
Make ahead: Assemble the cold sandwiches and wrap them in plastic wrap to store in the refrigerator a few hours before you plan on grilling them.
Hot or cold: Yes, a Reuben is also delicious cold (without grilling it).Try it if you're in a hurry or don't want to dirty a skillet.
Montreal-style: Trade in Montreal smoked meat for the beef brisket for a Montreal Reuben.
Walleye Reuben: Try walleye pike fillets instead of beef for a pescatarian-friendly reuben.
Rachel: Craving pastrami or turkey rather than corned beef? Voila, you've got a Rachel.
Egg rolls: For a riff on this popular flavor combo, take inspiration from a menu item made famous at Mader's in Milwaukee, WI: deep-fried egg rolls stuffed with corned beef, Swiss, and sauerkraut, served with a side of thousand island dressing for dipping.
Serve with: Reubens are best enjoyed with the cold slices of kosher pickles, crunchy potato chips, plus sides of coleslaw and macaroni salad, plus strawberry cheesecake bars for dessert.