Instead of cooking the beef in a frying pan (which can be messy) its perfectly possible to cook the carne asada in the oven. Get the oven extremely hot (220c) and place the meat in the oven. After 15 mins turn the oven down to 180c and cook for a further 20 mins per 500g.
The hot oven at the start sears the meat and creates a maillard reaction which really adds to the flavour or the meat.