Combine the beef, breadcrumbs, milk, garlic, 1/2 teaspoon salt, and pepper to taste in a large bowl and knead the mixture together with your hands. Roll into heaping-tablespoon-size balls.
Heat 2 tablespoons olive oil in a large nonstick skillet over medium heat. Add the onion and cook, stirring, until slightly softened, about 2 minutes; remove to a plate. Heat the remaining 1 tablespoon olive oil in the skillet over medium heat. Add the meatballs and cook, turning, until browned all over, about 1 minute. (You might have to do this in 2 batches.)
Pour in the marinara sauce and return the onion to the skillet; gently stir. Cover and simmer 20 minutes.
When ready to serve, split the dinner rolls and sprinkle some mozzarella on the bottom rolls. Top each with a meatball, some sauce and more mozzarella and sandwich with the top rolls.