Restaurants recommendations in Vatican area that aren't sandwich shops

We liked Il Mozzicone on Borgo Pio. Tourists are there but also locals. You can eat outside or in.

This restaurant is excellent:
la Soffitta Renovatio
Piazza Risorgimento 46 A, 00192 Rome, Italy

It is very close to the Vatican and St. Peters.

They cater to both the gluten-free and "non-gluten-free" diner. Most of the wait staff speaks excellent English although by no means do you feel like you are dining in a tourist trap. Excellent homemade desserts besides the usual pizza, pasta, meat dishes, etc. We ate there 4 days in a row we liked it so much. The owner is charming and welcoming.

Do your snacking at Antonini's pasticceria -- this is where the people who work in the court building (lawyers, legal assistants, detectives) hang out in the late afternoons.

http://antoniniroma.it

They have very fresh fancy small bites, both savory and sweet, to go with wine and aperitivos --
if she's still there, the dessert chef knows enough English to help you put together a picnic tray;
if she isn't there, you can practice your food vocabulary and charade skills.

Wow, just looking at their menu makes me want to get back there now!

We ate at Trattoria da Marcello, a priest we know recommended it.

Ristorante Arlu, on Borgo Pio.

Thank you all for the feedback. Amazingly, the first response brought to mind a restaurant we enjoyed in 2012 while on our first trip to Rome. It's wonderful to find that others are still appreciating your special discoveries from years gone by.

La Rustacella, Via Angelo Emo, near Cipro metro