Whisk the brown sugar into the chicken broth until it's dissolved. Next, whisk the soy sauce in and set it aside.
Slice the carrots, broccoli, and onion into 2-inch pieces. Slice the chicken into similar-sized strips.
Preheat a wok with oil and sauté the chicken until it's golden brown. Remove the chicken from the skillet and set it aside.
In the same wok, sauté the onions in the chicken drippings and a bit more oil until golden brown. Remove the onions from the skillet and set aside. Next, sauté the carrots until softened, add in the broccoli, and sauté for an additional 3 minutes. Press the garlic into the wok.
Add the cooked chicken back into the wok with the veggies. Pour the sauce over the ingredients and simmer for about 2 minutes.
Add the cooked noodles, toss everything together, and enjoy!