Preheat oven to 350 degrees F. Spray an 11-inch rectangular baking dish with nonstick cooking spray.
Using a large serrated knife, slice the rolls in half so you have a “slab” of tops and a “slab” of bottoms; don't pull the rolls apart and slice individually because you want to keep them connected. Spread dijon mustard on each slab.
Layer the sliders as follows: half of the sliced cheese, then sliced ham, sliced turkey, and remaining cheese.
Replace the top half of the rolls.
In a small bowl, combine the melted butter with the egg and brush on top of the rolls.
Cover with loosely with foil (careful not to let it touch the tops of the bread to avoid sticking - use toothpicks if necessary to "lift" the foil).
Bake in a preheated 350 degree oven for 15 minutes. Remove foil and continue to bake for another 10 minutes or until tops are nice and golden brown.
Cool slightly, then cut the sliders apart with with a sharp knife. Sprinkle powdered sugar over the top, if desired, and serve hot with berry preserves on the side.