Position a rack in the center of the oven and preheat it to 375°F (190°C). Grease a 9-by-13-inch (23-by-33-cm) metal baking pan with the neutral oil. For easier removal, line the bottom with parchment paper, leaving a small overhang on two sides.

Place the sauerkraut in a fine-mesh strainer and press out as much liquid as possible. Transfer it to a clean kitchen towel or several layers of paper towels and squeeze firmly. The sauerkraut should feel moist but should not drip when pressed.

Unroll one crescent dough sheet and press it into the bottom of the prepared pan. Gently stretch it to the edges without tearing it. If using perforated crescent dough, pinch the seams closed.

Bake the bottom crust for 8 to 10 minutes, until it looks dry and lightly golden around the edges but is not fully browned. If the center puffs, gently press it down with the back of a spoon.

In a medium bowl, combine the dried sauerkraut and 3/4 cup Thousand Island dressing. Stir until the sauerkraut is evenly coated. The mixture should be creamy but not runny.

Arrange half of the Swiss cheese over the warm bottom crust, overlapping the slices slightly. Covering most of the crust with cheese creates a barrier between the dough and the moist filling.

Spread the corned beef evenly over the cheese, separating any pieces that are stuck together. Spoon the sauerkraut mixture over the meat and spread it into an even layer without pressing down heavily.

Arrange the remaining Swiss cheese over the sauerkraut. Keep the cheese slightly inside the edges of the pan so less of it escapes while baking.

Unroll the second crescent dough sheet over the filling. Gently stretch it toward the corners and pinch any perforations closed. Tuck or press the edges against the sides of the pan. Cut four small slits in the top to allow steam to escape.

Whisk the beaten egg with 1 tablespoon water. Brush a thin, even layer over the top crust. Sprinkle with the caraway seeds, if using.

Bake for 24 to 27 minutes, until the crust is deeply golden, the cheese is bubbling around the edges, and the center is hot. If the top browns too quickly, loosely cover it with foil for the final 5 to 8 minutes. The center should reach approximately 165°F (74°C) when checked with an instant-read thermometer.

Let the casserole rest in the pan for 10 minutes. This allows the filling to firm slightly and makes the crust easier to cut. Slice into 8 portions and serve warm with additional Thousand Island dressing, if desired.