For the meatballs: Preheat the oven to 450 degrees F.
Combine the cheese, breadcrumbs, milk, oregano, lemon zest, salt and egg in a medium bowl. Add the pork and mortadella and gently fold the mixture until fully and evenly combined.
Drizzle 2 tablespoons olive oil on a small rimmed baking sheet. Scoop the mixture into 12 golf-ball sized balls and roll until smooth. Place on the baking sheet. Drizzle with the remaining tablespoon olive oil and bake, 15 minutes.
For the sauce: Meanwhile, pulse the pistachios in a food processor until coarsely chopped. Add the basil, parsley and salt and pulse to combine. And the olive oil and 1/4 cup cold water and puree until it's a relatively smooth paste. Add the cheese and pulse to combine.
Remove the meatballs from the oven and spread a teaspoon of pesto on each meatball. Bake for an additional 5 minutes.
For the sliders: Spread a little pesto on the top and bottom of each bun. Place a pinch of arugula on the bottom and a meatball on the arugula. Top with the top half of the buns and serve.