Grilled Reuben Sandwiches

1 cup Thousand Island dressing, divided
18 slices rye bread
12 slices Swiss cheese
½ cup canned sauerkraut, drained
24 slices thinly sliced corned beef  ( about 1 pound)
Butter, softened

Spread 2/3 cup Thousand Island dressing on one side of 12 slices of bread; arrange 1 slice cheese, 2 tsp sauerkraut, and 2 slices corned beef evenly over each slice.  Stack to make six (2 layer) sandwiches; spread remaining 1/3 cup dressing on remaining 6 bread slices, and invert on top of sandwiches.

Spread butter on outside of top slice of bread; invert sandwiches onto a hot skillet or griddle.  Cook until bread is golden.  Spread butter on ungrilled side of sandwiches; carefully turn, and cook until bread is golden and cheese is slightly melted.  Secure sandwiches with wooden picks; cut crosswise into thirds.  Serve hot.