I've been trying to find their business card but without luck. This was a very memorable experience, and I really want to recall the name of this restaurant. All I remember was walking down for maybe 10 minutes from Spanish steps (left literally behind my back), then turning left and walking another 4-6 blocks. Then we stopped at the pharmacy, and right after walking out within two-three blocks radius there was a small door (can't remember of there was any sign at all) in the very small street. When we walked in it looked like traditional Roman place with 90 years old waiters serving patrons. Two very small dining rooms if I can recall, and most of patrons were on business lunch wearing business suits. I thought the waiter could not believe his eyes seeing us walking in in jeans and comfy shoes. They did serve us, and it was quite expensive place. One appetizer, two pastas and a bottle of inexpensive wine was around 70-80 euro. The food was out of this world, and I still don't understand why we did not order artichokes - the table next to us ordered a huge plate, and it looked so good:)
I would certainly appreciate any ideas of what this place could be!