Prep. Preheat oven to 350º F. If not precut, then cut the rolls in half making a top and a bottom. Place the bottom half of the rolls into the baking dish.
Make the spread. Whisk together the ingredients for the spread in a small mixing bowl. Set aside.
Assemble the sandwiches. Place the ham on the rolls and add the cheese. Place the top of the rolls onto the assembled sandwiches. Spread the butter spread on top of the rolls.
Bake. Cover the baking dish with foil and bake in the preheated oven for 15 minutes. Remove the foil from the baking dish and continue to bake until golden brown and the cheese has melted, about 10 more minutes.
Serve. Remove from the oven and slice around the edges of the rolls through the ham and cheese to easily serve. Serve warm.
