Place the chicken in a large mixing bowl and allow to sit at room temperature for thirty minutes to an hour.
Whisk together the milk and egg. Stir the bread crumbs into the milk mixture and allow to soak for a minute or so until it resembles a thick porridge. Add the bread crumb mixture to the chicken, along with the parsley, garlic, shallots, salt, mustard, oregano, and mozzarella cheese. Season generously with freshly ground black pepper. Toss gently with your hands to mix ingredients until just combined. It will be a little wet. Cover and refrigerate, if desired.
Fill a spring-form ice cream scoop with meat mixture. Release the ball and gently pat into a cohesive ball. Arrange on a parchment-lined baking sheet and continue with remaining meatballs. It's okay if the meatballs are touching.
Bake the meatballs until they reach an internal temperature of 160°F, about 15-20 minutes. Switch oven to broil and cook for another 2-3 minutes, until golden-brown. Remove from the oven and allow to rest for a few minutes.
To assemble the sliders, place a layer of arugula on the bottom half of roll. Top with a warm meatball, a drizzle of tomato sauce, and a generous sprinkling of Parmesan and black pepper. Cover with top half of roll and secure with a toothpick if desired. Serve immediately