Step 1
Gently mix 2 large eggs, 1 lb. ground beef, ½ cup plain fine dried breadcrumbs, 3 garlic cloves, finely chopped, 2 oz. Parmesan, finely grated (about ½ cup), ⅓ cup finely chopped parsley, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt in a medium bowl until combined. Working one at a time, scoop out about 2 tsp. meat mixture and roll into balls. Transfer meatballs to a baking sheet.
Step 2
Heat 1 Tbsp. extra-virgin olive oil in a medium Dutch oven over medium-high. Carefully arrange half of meatballs in pot; cook, turning occasionally, until lightly browned, about 4 minutes. (Be careful not to overbrown or meatballs will be tough.) Transfer to a clean plate with a slotted spoon. Repeat with remaining meatballs. Spoon out all but 2 Tbsp. fat from pot.
Step 3
Reduce heat to medium. Add 1 medium onion, finely chopped, and remaining 3 garlic cloves, finely chopped; season with salt. Cook, stirring occasionally, until onion is translucent and edges are starting to brown, 5–7 minutes. Add one 32-oz. can tomato purée, 4 cups low-sodium chicken broth, and 2 cups water. Season with salt; bring to a boil. Add 6 oz. pastina and cook until al dente, 8–10 minutes.
Step 4
Return meatballs to pot and cook, stirring to distribute, until heated through, about 5 minutes. Taste and season soup with more salt if needed.
Step 5
Ladle soup into bowls; top with more Parmesan and parsley. (The soup will thicken as it cools; add up to ½ cup broth or water to adjust the consistency if reheating.)