Bring a large pot of water to a boil. Add noodles, stir to separate, and cook until very tender, 5 to 8 minutes or according to package instructions. Drain and rinse with cold water.
Meanwhile, thoroughly mix ginger, garlic, cornstarch, soy sauce, and chicken in a bowl. In another bowl, whisk together broth, peanut butter, vinegar, chili garlic sauce, chili oil, and sesame oil.
Heat a large (not nonstick) frying pan over high heat and swirl in canola oil. Add green onions and chicken mixture, stirring to break up the meat, until chicken is lightly browned and no longer pink, 4 to 5 minutes. Add bell peppers and stir for 1 minute. Add chicken broth mixture; stir until slightly thickened, 2 minutes.
Add snow peas and noodles to pan. With tongs, toss just until snow peas are brighter green and noodles are well combined and heated through, 1 to 2 minutes. Add 1/4 cup peanuts and toss. Top with more green onions and remaining peanuts, and serve with more chili garlic sauce and chili oil.
*Look for fresh or dried Chinese-style egg noodles at well-stocked supermarkets or Asian markets.
Wine pairing: A slightly off-dry white such as Zocker 2013 Paragon Vineyard Riesling (Edna Valley; $20), with vibrant florals that tame the heat. --Sara Schneider