In a large bowl, combine ground beef, grated Parmesan cheese, breadcrumbs, egg, minced garlic, dried Italian seasoning, salt, and black pepper. Mix until just combined.
Form the mixture into 1-inch meatballs and set aside.
Heat olive oil in a large deep skillet or pot over medium heat.
Add the chopped onion and cook until softened, about 3 minutes.
Add the meatballs to the pot and brown on all sides, about 5 minutes, turning carefully to avoid breaking them. They do not need to be fully cooked at this stage.
Pour in the marinara sauce and water, stirring gently to combine.
Add the uncooked penne pasta and red pepper flakes, making sure the pasta is submerged in the liquid.
Bring the mixture to a boil, then reduce heat to medium-low and cover the pot.
Simmer for 15 to 20 minutes, stirring occasionally, until the pasta is tender and the meatballs are cooked through.
Remove from heat and stir in the chopped fresh basil.
Serve hot, garnished with additional Parmesan cheese if desired.