Preheat the oven to 350°F (175°C) and coat a 9x13-inch baking dish with non-stick cooking spray.

Spread 3 cups of the rye bread cubes across the bottom of the prepared baking dish in a uniform layer.

Distribute the diced corned beef evenly over the bread cube base.

Layer the prepared sauerkraut over the corned beef, ensuring even coverage.

Apply 2 cups of shredded Swiss cheese as the next layer.

In a medium mixing bowl, whisk together the Thousand Island dressing and whole milk until homogenized; pour this mixture evenly over the cheese and sauerkraut layers.

In a separate bowl, toss the remaining 3 cups of rye bread cubes with the melted butter and caraway seeds until coated.

Distribute the buttered bread cubes over the top of the casserole and sprinkle with the remaining 1 cup of Swiss cheese.

Place the dish in the center of the oven and bake for 35 minutes, or until the internal temperature reaches 165°F and the cheese is golden and bubbling.

Remove from the oven and allow the casserole to set for 10 minutes before portioning and serving.