Preheat oven to 375°F (190°C).
In a large bowl, combine ground beef, Italian-style breadcrumbs, 1/4 cup grated Parmesan cheese, egg, 2 cloves minced garlic, chopped parsley, salt, and black pepper. Mix until just combined.
Form the mixture into 16 evenly sized meatballs, about 1 inch in diameter.
Place meatballs on a baking sheet lined with parchment paper and bake for 15 minutes until browned and cooked through.
While meatballs bake, warm marinara sauce in a medium saucepan over low heat.
Add cooked meatballs to the marinara sauce and simmer gently for 10 minutes.
In a small bowl, mix softened butter with 3 cloves minced garlic.
Spread the garlic butter mixture evenly on the cut sides of the hoagie rolls.
Place the rolls on a baking sheet, buttered side up, and toast in the oven for 5 minutes until golden and crispy.
Remove rolls from the oven and spoon meatballs and marinara evenly into each roll.
Top each sub with shredded mozzarella cheese and sprinkle with 1/4 cup grated Parmesan cheese evenly over all subs.
Return the assembled subs to the oven and bake for an additional 5 minutes or until the cheese is melted and bubbly.
Remove from oven, garnish with chopped fresh basil if desired, and serve immediately.