Preheat oven to 375°. Get all of the slider ingredients out and organized near your cutting board. Line one or two sheet pans with parchment paper. You may be able to fit both packages on one tray.
Carefully cut the cluster rolls in half long ways. This will leave you with a block of tops all together and a block of bottoms all together. Do not separate the package into individual rolls.
Lay the bottoms on a sheet pan and begin to assemble the sliders.
First, spread a generous amount of aioli evenly over the bottoms. Then make a layer of salami, then ham, then turkey. Next make a layer of sliced provolone. Be sure to overlap a little so that every slider gets good cheese coverage. Last spread the muffaletta over the provolone.
Put the tops back on, try to line them up at the corners. Drizzle or brush melted butter over the top and then sprinkle with Parmesan cheese.
Bake on 375° for 20 minutes. Let cool for 5, then cut into 24 individual sliders and serve.