Adjust an oven rack to the middle position and preheat to 350°F
In a small bowl, whisk together all of the ingredients for the butter sauce. Set aside.
Using a serrated bread knife, slice the rolls in half horizontally, keeping the top and bottom halves separately intact. Spread the Dijon mustard evenly over the cut sides of the roll tops and bottoms.
Place the bottom half of the bread, cut side up, in a 9-inch square baking pan. Place half of the cheese in an even layer over the bread. Top with all of the ham, followed by the remaining cheese. Cover with the roll tops.
Evenly spoon the butter sauce over the top of the rolls, letting it drip down the sides.
Bake for 22-25 minutes, until the top is golden brown and toasted. Let cool for 15-20 minutes in the pan. Using a large spatula, carefully transfer the sandwich block to a cutting board. Slice into sandwiches and transfer to a paper towel-lined serving plate. Serve warm or room temperature.