Pulse pistachios, basil, Parmesan and garlic in a small food processor until finely chopped. Add olive oil, lemon juice and pepper and pulse just until a thick, slightly textured pesto forms.
Spread drained ricotta evenly over the bottom focaccia halves and pistachio pesto over the cut faces of the tops.
Fold mortadella loosely over the ricotta, dividing it evenly between the sandwiches. Add dry arugula without packing it tightly.
Close with the pesto-spread tops and cut each sandwich across the middle. Serve cold or refrigerate promptly at 40°F or below, transporting with ice packs.