Whisk the brown sugar into the chicken broth until it's dissolved. Next, whisk the soy sauce in and sesame oil, set it aside.
Slice the carrots, broccoli, into 2-inch pieces. Slice the chicken into similar-sized strips.
(You don't need oil on this step, but you should salt and pepper here) Preheat a wok with oil and sauté the chicken until it's golden brown. Remove the chicken from the skillet and set it aside.
Next, sauté the carrots and broccoli, and sauté for an additional 3 minutes. Add the garlic, ginger and snow peas into the wok.
Add the cooked chicken and 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, garnish with green onions and enjoy!
