Prepare the ingredients by cutting the flank steak into strips. Cut across the grain, and make each strip about a quarter inch wide and three or four inches long. Cut the onions and carrots into about the same size pieces.
Put the olive oil into the skillet and heat it on medium heat. When the oil has heated for a bit (you should start to smell it), drop in half the onions and about a quarter of the beef. Add in 1 tbsp of Worcestershire sauce, and stir so that the beef cooks evenly.
Once the beef has cooked on all sides, take it out of the skillet and put it into the mixing bowl. Add more meat to the skillet, and continue.
When the onions are tender, remove them as well and add in the rest of the onions.
You should have cooked all the beef fairly quickly. Note that it isn't necessarily done all the way through, but the outside is done. Once the last of the beef is out, put in all the carrots and the other tablespoon of Worcestershire sauce.
When the second onion is done, remove it into the mixing bowl. When everything but the carrots is in the mixing bowl, toss the meat and onions, then dump them back into the skillet.
Cover and cook for another five or ten minutes, mixing occasionally. The carrots should end up firm, not mushy. Turn the heat off but leave covered until you're ready to serve.
This goes great with rice, and the onions pick up the flavor of the Worcestershire sauce for a great combination.