Preheat the oven to 375 degrees F. Line a baking sheet with parchment paper.
Unfold the sheet of puff pastry and roll into an 11-inch square. Using a pizza wheel or sharp knife, slice the dough into 1/2-inch-thick strips. Wrap each baton of mortadella in one strip of puff pastry, overlapping the dough slightly with each wrap-around to create a spiral appearance in the dough while leaving the mortadella ends exposed.
Place the rolls on the prepared baking sheet, spaced 1 inch apart. Brush each roll with egg and top with a good pinch of Gruyere. Bake until golden brown and puffed, 25 minutes.
Serve warm, with mustard if desired.