Step 1: Prepare the Chili Oil. Heat neutral oil in a small saucepan over medium-low heat. Add Szechuan chili flakes, minced garlic, grated ginger, Szechuan peppercorns, and a pinch of salt. Cook gently for 8-10 minutes, ensuring the garlic doesn't burn, allowing the flavors to infuse. Remove from heat and let cool slightly. Strain if desired, or leave all aromatics in.
Step 2: Marinate the Steak. In a bowl, toss the thinly sliced flank steak with soy sauce and cornstarch. Let sit for at least 10 minutes while you prepare other components.
Step 3: Cook the Noodles. Bring a pot of salted water to a boil. Cook noodles according to package instructions until al dente. Drain well and set aside.
Step 4: Cook the Steak. Heat 1 tablespoon of oil in a large skillet or wok over medium-high heat. Add marinated steak in a single layer and sear quickly for 1-2 minutes per side until browned and cooked to your liking. Remove steak from skillet and set aside.
Step 5: Fry the Eggs. In the same skillet, add a little more oil if needed. Crack in the two eggs and fry sunny-side up until the whites are set and the yolks are still runny, about 2-3 minutes.
Step 6: Assemble the Dish. In a large bowl, add the cooked noodles. Drizzle generously with the prepared Szechuan chili oil (start with 2-3 tablespoons and add more to taste). Toss to coat thoroughly.
Step 7: Serve. Divide the noodles into two serving bowls. Top each with seared steak slices, a fried egg, chopped scallions, and sesame seeds (if using). Serve immediately.