Instead of being simmered in a tomato sauce, the meatballs for these tasty sub sandwiches get tons of flavor from a tangy-sweet glaze made with balsamic vinegar and chicken broth. A splash of soy sauce gives the glaze a touch of umami while the melted provolone cheese and peppery arugula in the subs round out all the flavors.
Combine the turkey, breadcrumbs, parsley, scallions, garlic, salt and pepper in a large bowl and mix well. Using a 2-tablespoon scoop, scoop lightly packed mounds of the mixture onto a plate or baking sheet, then roll them into neat balls.
Heat the olive oil in a large nonstick skillet over medium heat. Add the meatballs and cook, turning occasionally, until browned but not cooked through, 6 to 8 minutes.
Whisk the broth, vinegar and soy sauce together in a small bowl. Pour the mixture into the skillet with the meatballs and bring to a boil over high heat. Reduce the heat to medium and simmer, basting occasionally, until the meatballs are cooked through and the sauce has thickened, 8 to 10 minutes.
Meanwhile, preheat the broiler with a rack about 8 inches from the heat source. Arrange the split hoagie rolls on a large rimmed baking sheet and top each with 3 slices of provolone. Broil until the cheese is melted and the buns are lightly toasted on the edges, 1 to 2 minutes. Fill the rolls evenly with the arugula, if using, and the meatballs, spooning some of the sauce on the subs. Top with Parmesan or pecorino, sprinkle with parsley and serve.