Cook noodles according to package instructions. Drain, rinse, then toss with 1 Tbsp oil. Set aside.
Whisk together eggs with the brown sugar. Set aside
Heat remaining 2 Tbsp of oil in a wok and saute garlic and green onions for a minute, then add the coleslaw mix. Cook until softened, about 2 minutes. Transfer to plate.
Add egg mixture to hot wok, and stir fry until scrambled and set. Transfer to plate.
For the sauce, whisk everything together then add to wok along with noodles, tossing to combine. Bring to a boil and allow to reduce slightly to a sauce-like consistency. Add eggs and veggie mixture, tossing to combine.
To serve, garnish with peanuts and lime juice.