It’s called Cantina das Freiras; it’s run by a local Catholic organization, and it’s one of those places that’s impossible to find if you don’t already know about it. Here’s a picture of the alley you’ll find it in (it’s the first door on the right — note the complete absence of any signage indicating a restaurant is here):
You go up a few flights of stairs, order your food cafeteria-style, then you’re free to carry your tray outside and take in the magnificent view.
I just pointed at the tray of the lady in front of me and asked for the same stuff (this is the sort of thing you have to do to save yourself the indignity of staring blankly back at a person after being asked something in a language you don’t understand).
So I wound up with a piece of pan-fried fish, some pretty basic potatoes, and a salad. The food was fine, if nothing particularly special, but it was only €6.50, and did you see that view? That alone is reason enough to come; the delightfully affordable food is just a bonus.