Preheat a grill pan or outdoor grill over medium-high heat.
Lightly make diagonal cuts both ways on the salami and mortadella, making sure not to cut completely through each slice. Grill the salami until it begins to get crisp and render some fat, 2 to 3 minutes. Then flip and top with a slice or 2 of muenster to fit. Grill until the muenster melts, 2 to 3 minutes. Remove from the pan and slice into 4 pieces to fit 4 slider buns. Repeat the process with the mortadella.
Smear the buns with the mustard. Top 4 of the buns with 1 slice grilled salami and a few chips. Repeat with the mortadella and remaining buns. Serve to the kids but watch the adults try and eat them all.