Preheat the oven to 375°F (190°C).
In a large bowl, combine ground beef, grated Parmesan cheese, breadcrumbs, egg, minced garlic, dried Italian seasoning, salt, and black pepper. Mix until all ingredients are evenly incorporated.
Form the mixture into 16 meatballs, about 1 1/2 inches in diameter each.
Place the meatballs on a baking sheet lined with parchment paper and bake for 15 minutes.
While the meatballs bake, warm the marinara sauce in a medium saucepan over low heat.
Remove the meatballs from the oven and transfer them to the marinara sauce. Simmer on low heat for 10 minutes to allow flavors to meld and meatballs to finish cooking.
Meanwhile, slice the sub rolls lengthwise without cutting all the way through, creating a pocket.
In a small bowl, mix the softened butter with minced garlic and chopped fresh parsley.
Spread the garlic butter mixture evenly inside each sub roll.
Place the buttered sub rolls on a baking sheet and toast in the oven for 5 minutes until golden and crispy.
Remove the toasted rolls from the oven and spoon 4 meatballs with marinara sauce into each roll.
Top each sub with 2 ounces of shredded mozzarella cheese.
Return the assembled subs to the oven and bake for an additional 5 minutes, or until the cheese is melted and bubbly.
Remove from the oven and serve immediately.