Organic steak in Barcelona
Don't know about organic but traditionally reared should not be a problem at quality restaurants. Veal from Galicia and girona is traditionally good.
My favourites though work with Argentine beef. La Pampa in Castelldefels (15 km to the south of the city) is a great example. Nothing fancy and they do not know how to cook but they are great with the parilla (grill).
More fancy and in town, Agora at Sepulveda 76, whom serve the steak in filo pastry with gorgonzola cheese. Aprox. 17 euros + vat if memory is not failing me.