How to Make It
In a small bowl, mix together the soy sauce, grated ginger, red pepper, 3 tablespoons each of the vinegar and brown sugar, and 2 tablespoons of the oil. Pour two-thirds of the dressing into a shallow baking dish, add the steak, and refrigerate, turning once, for at least 1 hour and up to 12 hours. Set aside the remaining dressing.
In a small saucepan, bring to a boil ½ cup water, the remaining ½ cup of vinegar, the remaining tablespoon of brown sugar, the sliced ginger, and ½ teaspoon salt. Add the carrots and jalapeño and simmer until the carrots are crisp-tender, 1 to 2 minutes. Transfer the mixture to a bowl and refrigerate until cool, at least 1 hour.
Fifteen minutes before serving, cook the noodles according to the package directions; rinse.
Meanwhile, heat the remaining tablespoon of oil in a large skillet over medium-high heat. Cook the steak to the desired doneness, 4 to 6 minutes per side for medium-rare. Let rest 5 minutes. Slice and serve on the noodles with the pickled vegetables, cilantro, and reserved dressing.