Cook the Mortadella: Heat a large frying pan over medium heat and add olive oil. Place the slices of mortadella in the pan and fry until crispy on both sides, about 2-3 minutes per side.
Melt the Cheese: Stack the crispy mortadella in the pan and top with provolone cheese. Add a splash of water (about 1 teaspoon) to the pan and cover with a lid to create steam. Let it cook until the provolone cheese is melted, about 1-2 minutes.
Toast the Buns: While the mortadella cooks, toast the brioche buns until golden brown.
Assemble the Sandwich: Spread mayonnaise on the bottom half of each toasted bun and Dijon mustard on the top half. Place the stack of mortadella with melted provolone on the bottom bun, then top with the mustard-spread bun half.
Prepare the Drink: In a glass, mix the sparkling water with sliced lemon. Serve over ice if desired.
Serve: Plate the sandwich with sliced apples and creamy peanut butter on the side.