Preheat the oven to 350°. Remove the rolls from the package without separating them. Slice the sheet of rolls in half at the equator. Place the bottom sheet in a 9x18 baking dish.
Arrange the ham over the bottom of the rolls. If using deli ham, I like to wad it up to create some thickness. If using leftover ham, Arrange the pieces so the entire sheet of rolls is covered evenly. Arrange the cheese on top of the ham. Put the top half of the rolls on top of the cheese.
Using a serrated knife, carefully cut between the sandwiches.
Combine the remaining ingredients and brush over the sandwiches. Make sure some of the butter mixture gets in between the sandwiches. Use all of the butter mixture.* Let the sandwiches sit for at least ten minutes to allow the butter mixture to soak in. Bake for 20 minutes or until the cheese is all melted and the tops are golden brown.
Notes
*You can make the sandwiches to this point, cover, and refrigerate for a day or two.