Remove the steak from the refrigerator, discarding the marinade. Heat 1 Tablespoon olive oil in a large skillet over medium heat until shimmering. Add half the meat in a single layer and cook for one minute without stirring, until browned on one side.
Remove the steak from the freezer and slice thinly against the grain. Add the steak to the large plastic bag with the marinade and refrigerate at least 10 minutes or up to 1 hour.
Meanwhile, combine honey, vinegar, soy sauce, and Worcestershire sauce in a medium bowl. Measure out 1/4 cup of this sauce and pour it into a large zipper-top plastic bag or glass bowl for marinating the meat. Reserve the remaining sauce for the stir-fry.
Freeze steak for 15 to 20 minutes, just until the outside is chilled but the steak is not frozen solid. This will make it easier to slice the steak thinly.