Cut all rolls in half, making buns with tops/bottoms. (Easiest to do all at once; keeping bottoms connected as one unit). Place bottoms of rolls in a rimmed baking dish pan, sprayed with Pam.
Place equal amounts of ham on each roll bottom.
Top with slice of cheese.
On the cut-side of the roll TOPS, spread ~ 1 Tbs. of chive/onion cream cheese (again, just keep them all connected). Return bun tops to the bottoms, making a sandwich. (At this point, I slice through sections to finish separating individual sandwiches, so topping can drizzle down).
Combine the melted butter, onion flakes, and Worcestershire sauce. Spoon this over top of each sandwich. Sprinkle tops with Parmesan. Cover with aluminum foil and refrigerate for AT LEAST 30 minutes – up to overnight.
Preheat oven to 350. Bake sandwiches (covered in foil) for 20-25 minutes, until golden on top and Gruyére is melted. Optional: Sprinkle with chopped fresh chives & insert a leaf of baby spinach in each. Serve immediately.