Could this simply be referring to a "Mesón Asador" restaurant, which wouldn't need translated.

See
http://www.mesondelasador.com/home.htm

en la red a establecimiento españoles así definidos

In my experience, a Spanish 'Meson Asador' tends to have a very traditionally rustic appearance and plenty of slowly roasting meat. Exposed ceiling beams are practically a legal requirement.

Not the ideal place for vegetarians or non-smokers.

This is perhaps a peculiarly Spanish speciality (although the restaurant called Roast in Borough Mkt in London is setting a trend), a restaurant which serves mainly roast meat dishes.

I'm presuming that we are referring to the restaurant in an explanatory way - this obviously wouldn't do as a name.

Mesón is another thing - if they really are old establishments, then they fit the DRAE definition mesón1.

(Del lat. mansĭo, -ōnis, con infl. del fr. maison).


1. m. Establecimiento típico, donde se sirven comidas y bebidas.

although nowadays there are many pseudo-typical places springing up, in particular in the Castilian style (I'm thinking of the centre of my city, Avila). These places would probably style themselves as "eateries" to emphasize their traditional style, but I don't like the term myself! Take it if you want!

Vegetarians beware!

:)