Peel the carrots, potatoes and onion, then roughly chop into chunky cubes. Add them to a large saucepan, cover with about 800 ml–1 litre of water, and bring to the boil. Stir in the tomato paste and season with salt and pepper.
Once the vegetables are soft, scoop them out of the pot using a slotted spoon or colander, keeping the cooking water in the saucepan. This liquid is now a simple homemade vegetable stock — set the pot aside for a moment.
Transfer the vegetables to a bowl and blend with a hand blender until smooth and creamy.
Bring the reserved stock back to a gentle boil, add the pastina, and cook for 5–6 minutes, or until tender.
Finally, pour the blended vegetables back into the same pot, stir well, and cook for another minute until everything is beautifully creamy and combined.
Serve warm with grated Parmesan and a drizzle of good-quality extra virgin olive oil.