Gently combine beef, breadcrumbs, Parmesan, egg, garlic, Italian seasoning, salt, and pepper. Shape into small, evenly sized meatballs.
Heat olive oil in a deep pot over medium heat and brown the meatballs on several sides, turning when they release easily. Transfer to a plate; they will finish cooking in the sauce.
Pour tomato sauce into the pot, add dry pasta, and add enough water to keep the pasta submerged. Bring to a gentle simmer.
Return meatballs immediately, cover, and simmer gently, stirring carefully and adding water as needed, until pasta is tender and beef meatballs reach 160°F at their centers. Use the pasta package time as a starting point; ground-poultry meatballs need 165°F.
Stir in basil and adjust salt and pepper. Loosen with water or briefly simmer uncovered if needed, then divide into four portions.