Pour vinegar into small saucepan and cook until reduced to 3 tbsp, about 5 minutes. Set aside.
Melt butter in a small saucepan over medium heat. Whisk in flour and cook (stirring constantly) for 1 minute. Slowly whisk in chicken stock and cook until thickened, about 2 minutes. Set aside to cool.
Run mortadella in a food processor until pureed. Transfer to medium bowl. Fold in whipped cream and cooled chicken sauce. Set aside.
Grill the ciabatta bread. Smear mortadella over warm bread, and drizzle with olive oil. Garnish with pistachios, arugula, and a drizzle of the balsamic reduction.