Whisk tomato sauce, beef broth, Worcestershire, brown sugar, and Italian seasoning in a bowl; set aside.
Combine ground beef, rice, onion, garlic, milk, salt, pepper, and parsley in a large bowl until just mixed.
Shape the mixture into 1½-inch meatballs; you should get about 16–18.
Heat olive oil in a wide skillet or Dutch oven over medium heat. Brown meatballs on two sides, 2–3 minutes per side.
Pour the sauce around and over the meatballs. Gently turn to coat and bring to a simmer.
Cover, reduce heat to low, and simmer 30–35 minutes, turning once, until rice is tender and centers reach 160°F.
Rest 5 minutes. Spoon sauce over meatballs and finish with a sprinkle of parsley.