Step 1

Place sliced chiles in a small bowl and cover with 2 tablespoons vinegar.

Step 2

Bring a large pot of water to a boil; remove from heat. Stir in noodles; let soak until softened (but still undercooked), 2 minutes. Drain; rinse under cold water until cool. Crack eggs into a bowl. In a separate bowl or measuring cup, stir together sweet soy sauce, soy sauce, and remaining 4 teaspoons vinegar.

Step 3

Preheat a large cast-iron skillet over high until very hot, about 2 minutes (a sprinkle of water should evaporate immediately). Add 1 tablespoon oil and swirl to coat sides and bottom. Add steak, spreading into a single layer. Let sear (do not stir) until golden on bottom, about 1 minute. Toss and turn occasionally until golden on all sides and just cooked through, about 1 1/2 minutes more. Transfer to a plate.

Step 4

Reheat skillet over high. Add remaining 2 tablespoons oil and swirl to coat sides and bottom. Add eggs and immediately scramble for 20 seconds. Add Broccolini and garlic and cook, stirring occasionally, until just tender, about 1 minute. Add drained noodles, seared steak and accumulated juices, and soy sauce mixture. Toss to coat. Cook 4 minutes, stirring every minute and allowing the sauce to sit and caramelize in between stirring. Serve with pickled chiles.