Heat 1 Tablespoon olive oil in a small saucepan over medium heat. Add the minced garlic, 1/4 teaspoon dried oregano, 1/4 teaspoon onion powder, and 1 pinch red pepper flakes and cook until fragrant. Add 24 ounce tomato puree, 2 Tablespoons water, 1/2 teaspoon dried basil, and 1/2 teaspoon kosher salt. Bring to a boil, then reduce the temperature and simmer until the tomato sauce is slightly thickened and reduced, about 10-15 minutes. Set aside.
Meatball Subs
While the tomato sauce is simmering, you can start assembling the meatball subs. Cut the rolls partway through (I prefer to cut straight through the top of the roll, as it makes it easier for the rolls to stand up while broiling). Butter the inside of each roll with approximately 1/2 Tablespoon of butter.
Add about 1/2 cup of arugula to the roll (if using), then put the meatballs on top (you will need 3-5 meatballs per roll, depending on the sizes of the rolls and the meatballs). Spoon about 1/4 to 1/2 cup of tomato sauce over the meatballs, then spread about 1/2 cup of mozzarella on top of the sauce. Top with about 1/2 Tablespoon of shredded Parmesan.
Turn on the broiler and move the oven rack to the middle positition. Put the sandwiches on a baking sheet lined with foil or parchment paper. Broil the subs until the cheese is melted and just starting to brown, making sure to watch them closely while they're broiling to make sure they don't burn. Serve immediately.