Preheat your oven to 350°F (175°C).
In a large mixing bowl, whisk together the eggs, milk, Dijon mustard, salt, and pepper until well combined.
In the 9x13-inch baking dish, layer half of the rye bread cubes on the bottom.
Add half of the sliced corned beef over the bread layer.
Spread half of the sauerkraut over the corned beef.
Sprinkle half of the shredded Swiss cheese on top of the sauerkraut.
Repeat the layers with the remaining ingredients: bread cubes, corned beef, sauerkraut, and Swiss cheese.
Pour the egg and milk mixture evenly over the layered ingredients, pressing down gently to ensure everything is soaked.
If using, sprinkle the caraway seeds on top.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
After 30 minutes, remove the foil and bake for an additional 15 minutes, or until the top is golden brown and the dish is set.
Allow the Reuben Layered Bake to cool for a few minutes before slicing into portions and serving.