In a medium bowl, combine Parmesan cheese and seasoning mix. Set aside until ready to assemble sandwiches.
Brush 3 tablespoons softened butter on each (18x26x1-inch) sheet pan. For 50 sandwiches use three pans. Sprinkle about 1/4 cup seasoning mixture on top of butter. Place 20 slices of bread onto each sheet pan; 4 across and 5 down (50 servings one pan will have 10 slices). Top each slice of bread with 1 slice Swiss cheese and 1 slice American cheese. Cover with remaining bread slice.
Brush top of sandwiches with softened butter, approximately 3 tablespoons per sheet pan. Add seasoning mixture evenly to top of sandwich slices (about 1/4 cup).
Bake until lightly browned. Conventional oven 400°F for 15 to 20 minutes or Convection oven 350°F for 10 to 15 minutes. Do not overbake.
Serve as is, or cut each sandwich diagonally in half.