Combine green olives, Kalamata olives, red peppers, garlic, capers, olive oil, vinegar, oregano and ¼ teaspoon black pepper in the bowl of a food processor fitted with a blade attachment.
Process until finely chopped and spreadable. Transfer to a bowl and set aside.
Carefully separate the sheet of connected slider tops and sheet of connected slider bottoms. Spread Garlic Parmesan with Herbs Butter Snack Spread all over the bottom sheet, and the olive salad all over the top sheet. Use the back of a spoon to gently smoosh the olive salad into the bread.
Evenly layer ham, soppressata, mortadella, and provolone on the bottom sheet of buns. Quickly flip the top sheet and place on top of the cheese layer. Gently press down, then use a sharp bread knife to cut into individual sliders and serve.