Great Italian appetizers are less about technique and more about buying the right stuff. That's actually true of all cuisine. Mortadella, also called baloney because it comes from Bologna, is a wonderful cold cut, so smooth as it slides over your tongue when you have it sliced super thin. Sometimes it has pistachios in it. Robiola cheese is, to my way of thinking, the sexiest cream cheese of all time. It's from Piemonte. When he saw me putting this together, Michael couldn't resist chiming in with, "I love this, Batali is making baloney and cream cheese sandwiches." He had a point; you could use regular old baloney instead of mortadella, and cream cheese works too. You roll 'em up with a basil leaf, cook 'em up on a grill pan. Finito!
Preheat a gas grill or prepare a fire in a charcoal grill.
Lay the mortadella out on a work surface. Place 2 tablespoons of the cheese in the very center of each slice. Place a basil leaf on top of each mound of cheese. Fold the bottom of each slice over the cheese, then fold over the sides and roll the cheese up in the mortadella. Secure each with a toothpick.
Place the mortadella packets seam side up on the hottest part of the grill and cook until lightly charred on the bottom, about 2 minutes. Turn over and repeat on the second side, about 2 minutes longer. Transfer to a platter, and remove the toothpicks from each packet.
Brush the slices of bread with a little olive oil and grill, about 30 seconds per side. Place a mortadella packet on each piece of bread.
In a medium-sized bowl, toss the arugula with 3 tablespoons olive oil and then the vinegar. Season with salt and pepper, to taste, and pile the greens over the hot and delightful mortadella packets.