In a medium pot, heat olive oil over medium/low heat. Add the diced onion and minced garlic. Sauté until the onion is translucent, about 3-5 minutes.
Add the tomato puree and 1 cup of hot broth/water. Simmer for 10-15 minutes, stirring occasionally.
Add the pastina to the sauce and continue to cook, stirring often, for 5-7 minutes or until the pasta is al dente. Add more broth or water if necessary to keep the mixture from drying out.
Remove the pot from the heat and stir in the grated Parmesan cheese. Season with salt and pepper if needed.
Serve the pastina hot, garnished with fresh basil leaves and Parmesan cheese.