Step 1: Set up the grill for direct grilling and preheat to high. Brush and oil the grill grate.
Step 2: Carefully slice each hot dog almost in half lengthwise, cutting to but not through the bottom casing. Gently open up the hot dogs as you would a book so that they lay flat.
Step 3: Arrange the hot dogs on the grill grate on the diagonal to the bars of the grate, cut sides down. Grill, turning once with tongs, until cooked through, about 3 minutes per side.
Step 4: Grill the mortadella for about 1 minute per side. Grill the hot dog buns, cut sides down, until lightly toasted, 1 to 2 minutes.
Step 5: To serve, slather each bun with mustard. Place a slice of mortadella in each bun, then add a hot dog. Top with sauerkraut and pickle slices. Wherever you are, Dear, I hope you’re enjoying this.