We divide the onion and cilantro between two resealable plastic bags. We smash our garlic cloves with the backside of our knife, remove the peel, and mince. We add this (about 1½ tablespoons) to the bags. Next we juice the limes into the bags and add a little salt and pepper. We squish the ingredients around from the outside of the bags to mix, and set aside while we get the steaks ready.
We trim the london broil of excess fat and pound it with our meat mallet between two pieces of wax paper to make it about ½ inch thick. We add the sandwich steaks to one marinade bag (they are thin enough so as not to require a pounding), and we add the london broil to the other marinade bag. We coat all the pieces of beef well, seal the bags, and refrigerate them in a large bowl for about 3 hours.
About forty-five minutes before we want to eat, we remove the steaks from the fridge and set them aside in their bags to rid them of their chill.
After 20 minutes, we heat a large sauté pan over medium heat with 1 tablespoon of the oil. We remove the steaks from the bags, reserving the marinade. We pat the steaks dry with paper towels and sprinkle the london broil with salt and pepper.
When the oil is hot, we add the london broil to the pan. We cook on the one side for 4 minutes and then flip with tongs. We cook for another couple of minutes and remove it to a clean plate. We check the temperature, it is still on the rare side.
The pan has darkened, so we deglaze it with one of the marinade bags. We stir well to pick up the browned bits on the bottom of the pan and lower the heat to medium-low. We cook for a few minutes to soften the onions. We pour this into a medium-sized bowl.
We heat half a tablespoon of oil over medium heat and add the rare steak back to the hot pan. We cook for two minutes on one side and another minute on the other side and remove it to the plate. The temperature quickly rises to a medium-rare/medium doneness.
We heat the remaining oil over medium heat. We sprinkle the three sandwich steaks with salt and pepper and add them to the hot oil in one layer. We brown on one side for a minute and then turn with tongs. We cook for another half a minute (the steaks are very thin and easily overcook) and remove them to the cooked meat plate. We deglaze the pan with the rest of the marinade, cooking for a few minutes over medium-low heat.
We serve the steaks with the onions, slicing the london broil into thin slices.