Prep: 20 min. To make these ahead, cover sandwiches with a damp paper towel, place in a heavy-duty zip-top plastic freezer bag, and chill up to 2 hours.
Stir together first 3 ingredients. Spread mixture on 1 side of each bread slice. Divide turkey slices among 5 pumpernickel bread slices and 5 rye bread slices. If desired, top with Parmesan cheese. Top with arugula and remaining bread slices. Cut sandwiches in half, and secure with wooden picks, if desired.