1. Prepare noodles according to package directions.
2. Mix the soy sauce, peanut butter, tahini, lemon juice, brown sugar, garlic, ginger, and water together in a bowl.
3. Heat the oil in a large pan over medium heat. Add the broccoli and stir fry until the broccoli changes color. Add the peanut sauce and mix until it begins to thicken. (For softer broccoli, turn the heat down to low, cover, and continue to cook until the broccoli has softened.)
4. Add the cooked and drained noodles to the broccoli mixture. Drizzle sesame oil on top if desired. Mix until all the noodles are coated in sauce.