Chop the yellow or white onion, carrots, and celery into roughly equal-sized pieces.

In a large pot, heat olive oil over medium heat. Add the chopped onion, carrots, and celery, stirring for about 5 minutes until softened.

Pour in the chicken or vegetable broth and stir in the Parmesan rind. Bring to a boil, then reduce to a simmer for 15-18 minutes.

Transfer the mixture to a blender, adding some broth for smoother consistency. Blend until silky and smooth.

Pour the pureed mixture back into the pot and stir to combine with the remaining broth. Bring to simmer again.

Add the pastina pasta to the pot and cook for 7-9 minutes until al dente.

Season to taste with salt and pepper. Serve warm, garnishing with grated Parmesan cheese and parsley.