Using a serrated knife, halve buns crosswise; arrange, cut side up, on 1 to 2 parchment-lined baking sheets.
Divide olive salad evenly among bread halves, about 3 tablespoons per sandwich. (Be sure to include any oil from olive salad.) Layer bottom half of each bun with Swiss, pepperoni, capocollo, ham, mortadella, and provolone. Cover each with top half of bun, olive salad side down.
Gently press each sandwich down. Cover and refrigerate for at least 2 hours to let olive salad soak into bread. Quarter sandwiches, and secure with a wooden pick before serving.
Recipe by Louisiana Cookin' at https://louisianacookin.com/mini-muffulettas/