Place mayonnaise, minced garlic, lemon juice, and parsley into a small mixing bowl. Stir until well combined and let sit in the fridge for at least 10 minutes.
Begin by making your aioli sandwich spread.
Next, make a muffuletta, by roughly chopping hot giardiniera, olives, and roasted red peppers. Place them in a small bowl and set aside.
Gather all of your sandwich ingredients and place them on a cutting board or plate to form an assembly line.
Then, take your Hawaiian rolls and place them on a cutting board. Using a serrated knife, cut the cluster rolls horizontally through the middle. You will be left with a sheet of bottom buns and a sheet of top buns.
Next, place the bottom half of the buns on a baking sheet. Spread garlic aioli evenly over the bread.
Then, stack the deli meats and provolone cheese slices on the bread.
Next spread a layer of muffuletta over the top of the cheese.
Put the top half of the buns on the sandwiches.
Next, melt butter in a microwave safe bowl. Then, mix melted butter, grated parmesan and dry parsley to make the parmesan butter.
Baste the tops of the slider buns with the butter mixture.
Bake for 15-20 minutes, until the meat is warm, the cheese is melted and the buns are toasted.
Remove the sliders from the oven and let stand for 5 minutes. Use a serrated knife to cut the cluster rolls into individual slider sandwiches.
Serve hot or at room temperature.