Dumplings made of pieces semolina pasta used to garnish soup?

You're describing "Gnocchetti"!

Gnocchetti are small, pillow-like dumplings made from semolina pasta dough. They are often used as a garnish for soups, adding a delightful texture and flavor to the broth. They are typically served in a simple broth or with a light sauce.

Here are some other names for these types of dumplings:

* Gnocchetti sardi: A Sardinian variety of gnocchetti, known for its slightly larger size.

* Gnocchetti al pesto: A Ligurian dish featuring gnocchetti served with pesto sauce.

* Gnocchetti alla Romana: A Roman dish featuring gnocchetti served with a simple tomato sauce.

Let me know if you have any more questions about gnocchetti or other Italian pasta dishes!