In a small saucepan over low heat, cook scallion whites, vegetable oil, red pepper flakes, sesame seeds, stirring occasionally, until oil is sizzling and scallions are golden brown, 12–15 minutes; let chili oil cool in saucepan.
Meanwhile, cook Momofuku x A-Sha Soy & Scallion Noodles according to package directions and drain.
In a large bowl whisk both packets from noodles and add tahini, vinegar, soy sauce, sesame oil, sugar, and 2–3 tablespoons chili oil (depending on desired heat). Add noodles and toss to coat. Top with scallion greens ,drizzle with more chili oil and add a fried egg if desired.