Marinate the Steak: In a bowl or zip-top bag, combine steak with dressing, Worcestershire, garlic, onion, salt, pepper, and red pepper flakes. Marinate for at least 1 hour, or overnight.
Cook Steak: Heat a skillet on high. Add the steak mixture and sear undisturbed for 2–3 minutes. Stir and cook until fully cooked. Transfer to a fine strainer to remove excess liquid.
Cook Vegetables: In the same skillet, sauté mushrooms in 1 tbsp oil until golden. Remove, then sauté peppers and jalapeños in another tbsp of oil for 1–2 minutes. Set all aside.
Combine Filling: Add cooked steak, onions, mushrooms, and peppers to a food processor. Pulse a few times until roughly chopped. Stir in shredded cheese.
Assemble Egg Rolls: Place wrapper in diamond position. Add 2 tbsp of cheese, then ¼ cup filling. Fold and roll tightly. Seal edges with egg wash.
Fry: Heat oil to 350°F (175°C). Fry rolls in batches for 3–4 minutes until golden and crispy. Turn as needed. Drain on paper towels.
Serve Hot: Cut diagonally and enjoy with your favorite dipping sauce.