You will be making this sandwich long after the holiday turkey leftovers are done with. Roast turkey, arugula and sharp Cheddar along with cranberry mayo are layered between pumpernickel bread then cooked until toasted.
Mix cranberry sauce, mayonnaise and ginger in small bowl. Set aside. Spread butter on 1 side of each slice of bread. Place 4 of the bread slices, buttered-side down, on cutting board. Top with turkey, cranberry spread, arugula leaves and cheese. Cover each with second slice of bread, buttered-side up.
Heat large skillet on medium heat. Place 2 of the sandwiches in skillet. Cook 2 to 4 minutes per side or until bread is toasted and cheese is melted. Repeat with remaining 2 sandwiches.