This is a traditional dish from Castilla La Mancha. My grandmother used to make it quite often. One of my favourites.
Preserving the cod in salt gives to the fish a much better texture and flavour. Nothing to do with the fresh one.
The translation is a bit tricky. “Atascar” is to get stuck and “Burra” is a female donkey.
I like the idea of a dish being named after its sound. When you are making the dish, mashing the potatoes with the garlic, cod and olive oil, the sound it makes is the same of a donkey walking on muck.