Line two square baking dishes (or similar sized rectangular pans) with foil, making sure it overlaps the edges. With a serrated knife, cut the tops of the rolls apart from the bottoms and place 12 roll bottoms in each pan.
In one pan, layer 1 slice of ham, 1 slice of salami, 1/2 slice of Swiss cheese, and evenly divide the 1/3 cup of peppers onto all 24 roll bottoms. Finish layering the sliders with the remaining tops—a tip is to gently pull apart the rolls to allow the butter to seep in. Additionally, I tear the ham slices and cheese to fit onto one roll to make cutting and serving easier.
In the second pan, layer 1 slice of ham, 1/2 slice of Swiss cheese, and 2 dill pickle slices onto all 12 roll bottoms. Finish layering the sliders with the remaining tops—gently tear apart rolls if desired.
In a medium bowl, melt the butter, then whisk together with Dijon mustard, honey, and salt. Spoon the butter mixture over the tops of all 24 rolls, then cover with foil and bake for 20 minutes. When 20 minutes has passed, remove the top layer of foil and return to the oven for 10 more minutes.