Crumble or chop the chorizo as finely as you can.
In a large bowl, combine ground beef, chorizo, diced onion, and garlic cloves.
Mix well but don't overwork the meat.
Divide and shape the meat into 4 large patties, or 6 smallish patties (I made 6), 1/2 inch thick. With your thumb, make a small indent in the middle of each burger.
Preheat a heavy bottomed, non-stick pan to medium heat and melt the butter in it. Make sure it's heated fully!
Working in batches if necessary, add the patties to the pan cooking 5 minutes on one side, and then 4 minutes on the other for a medium rare burger.
Once cooked, top each burger with 1/2 tbsp of mayonnaise then top with the cucumber slaw.
Plate and serve!