Combine the first eight ingredients in a large bowl and stir to blend. Remove half of the marinade and reserve it in a separate bowl.
Blot the flank steak dry with paper towels, put it on a baking sheet, and place in the freezer to chill for 30 to 45 minutes, or until hard but still sliceable. (Chilling allows for very thin slicing.)
Cut the steak in half with the grain. Then slice across the grain into 1⁄8-inch-thick pieces. Transfer each slice to the large (not reserved) bowl of marinade.
Toss the meat and marinade to mix well. Cover with plastic wrap and refrigerate for 1 to 2 hours.
Heat 2 tablespoons of vegetable oil in a large skillet or wok over high heat, add the snow peas and carrots, and cook for 2 minutes, or until tender but still crunchy, stirring often. Transfer to a bowl.
Add the remaining 1 tablespoon of oil to the skillet, heat briefly, then add half of the meat, laying each slice across the skillet, and cook for 1 minute, without stirring, to sear. Cook for 2 minutes more, or until all signs of pink are gone, stirring often. Transfer the meat to the bowl of snow peas and carrots. Repeat, cooking the remaining meat without any additional oil. Add the first batch of meat and vegetables to the skillet.
Combine the cornstarch and the reserved marinade and whisk to blend. Pour into the skillet and cook for 2 to 3 minutes, or until hot and thick, stirring constantly. Serve hot.
Try using matchstick-cut green beans and a thinly sliced bell pepper in place of snow peas and carrots.