So this might be a shot in the dark; but I'm trying to recall where I ate at 2 years ago.
What I remember is;
The place has outdoor seating on a patio. There is a wooden (I think) structure around the outdoor tables, they are not straight on the street.
To enter the inside of the restaurant, you need to walk down a stair, to the basement of the building.
The restaurant is set within the town walls. It is not in a narrow street, but on a small piazza or on a wide street.
I believe it might be in the south-east 1/4 of the old town.
From the menu, I remember we had a dish with baccalà, and 1 dish with cheeses and honey.
Does this place sound anywhere near familiar?