My mother used to make this and her original recipe also called for beef lung – no longer permitted by Dept. of Agriculture. I added the cubed beef to make up the difference. I never saw this on a restaurant menu.
You can get the whole soufritte story here – La Cucina Povera
In the same pot, add more oil, sauté onion and garlic until soft. Add tomato paste and caramelize. Add stock, deglaze and stir well and add bay leaf. Return meat, mix with onion and add oregano. Simmer covered for 1/2 hour, adding more liquid if needed. Taste for seasoning. Add the browned calf liver at the end.