Cut the carrots, celery, onion, and potato into large chunks. This helps them soften quickly and blend easily later.
In a large pot, add chopped vegetables, garlic cloves, tomato sauce, and broth. Bring to a boil over medium-high heat, then reduce to a simmer. Cover with a lid and let cook for 20 minutes, or until vegetables are tender.
Once the vegetables are soft, use a slotted spoon to transfer them to a blender, leaving the broth in the pot. Blend until smooth to create a creamy purée. If the broth left is too thick, add little more water (or broth).
Bring the broth back to a boil. Add pastina, stirring occasionally to prevent sticking, and cook until just al dente according to package instructions. Be careful not to overcook, as pastina can become mushy quickly.
Once the pastina is cooked, stir in the pot the blended vegetables and olive oil. Season with salt and pepper to taste, adjusting the consistency with more water or broth if needed.
Scoop the soup out into bowls, then top with grated Parmesan cheese and a drizzle of olive oil. Serve warm for a cozy meal!