Marinate: Combine all marinade ingredients (except the onion) in a blender and pulse until smooth. Place the pork and sliced onions in a gallon bag, pour the marinade over, and refrigerate overnight.
Setup: Prepare your Big Green Egg for direct grilling at 350°F.
Make the Mop: Pour the leftover marinade and onions into a small saucepan. Bring to a boil for 5 minutes. Blend until smooth to use as a basting sauce.
Grill: Place the pork tenderloin on the grill. Cook for about 15 to 20 minutes, turning and basting with the mop sauce every few minutes.
Rest: Remove the pork when it reaches an internal temperature of 140°F. Let it rest for 10 minutes before slicing into thin medallions.
Assemble: Slice the slider rolls in half. Spread mustard and mayo on the bottom. Layer the sliced mojo pork, ham, salami, Swiss cheese, and pickles.
Glaze: Place the assembled sliders in a cast iron pan or on a baking sheet. Brush the tops of the buns with the garlic butter mixture.
Melt: Place the sliders back on the Egg (indirect setup preferred here, or use a raised rack) for 10 to 12 minutes until the cheese is melted and the tops are golden.
Serve: Pull from the grill and serve immediately with extra pickles on the side.