In a medium bowl, combine the ground turkey, breadcrumbs, Pecorino Romano cheese, egg, crushed garlic, minced parsley, and kosher salt. Gently mix everything together until well combined. Be careful not to overwork the mixture, as this can make the meatballs tough.
Form the mixture into approximately 30 meatballs, about 1 heaping tablespoon each. This size ensures they cook evenly and fit nicely in the soup.
Press the sauté button on your Instant Pot and lightly spray the inner pot with cooking spray. Allow it to heat for a minute, ensuring the spray covers the surface.
In batches, brown the meatballs for about 2 to 3 minutes on each side. You want a nice golden color to develop, which adds flavor to the soup. Once browned, carefully remove them and set them aside on a plate.
After browning the meatballs, clean the pot by removing any leftover bits. Then, add the olive oil to the pot and heat it up.
Add the chopped onion, chopped celery, chopped carrot, and minced garlic to the pot. Sauté the vegetables for about 4 minutes or until they become soft and fragrant. The onion should turn translucent.
Next, add the diced tomatoes, Parmesan rind (if using), basil leaves, and bay leaves to the pot. Stir everything together to combine.
Return the browned meatballs to the pot, nestling them among the vegetables and tomatoes.
Pour in the chicken broth, making sure to cover the meatballs and vegetables. Secure the lid on the Instant Pot and set it to cook on high pressure for 15 minutes.
Once the timer goes off, perform a quick release. Carefully open the lid and add the ditalini pasta and zucchini to the pot. Stir gently to combine.
Cover the pot again and cook on high pressure for an additional 4 minutes. This will allow the pasta to cook perfectly without becoming mushy.
After the time is up, do another quick release and open the lid. Stir the soup gently before serving.
Serve the soup hot, garnished with a sprinkle of grated parmesan cheese and additional basil leaves if desired.