Hadn't been able to find a restaurant open in early in the morning when suddenly, an internet search popped up with this restaurant showing 24-7 hours of operation. 

The tables were empty, and the bar nearly so. Raz informs me that the napkins etc. on the floor around the bar were a cultural thing, and I watched the speed and efficiency with which the tables were bussed. Thus, I'm interpreting the many little piles of napkins, etc at the bar as a testament to the popularity of the joint with locals.

There was a single bar tender running the whole front of the house. Between our broken Spanish and his limited English, we managed to order breakfast and coffee, which zipped out of the kitchen surprisingly quick. Raz ordered a combination plate that involved the best veal I've tasted to date. I ordered Tostas con Jambon Iberico, which was s phenomenal as it was simple, and easily worth more than the asking price.  While we feasted, enough locals came in to completely fill the bar and half the  tables in the place, reinforcing our opinion of popularity and quality. 

Last and most important for travellers  like us in a country with high exchange fees, they were able to accept credit cards.  All in all, a stellar breakfast that we would repeat, and the extra star for 24-7 accessibility.