Cook the Noodles: Bring a pot of water to a boil. Add the noodles and cook according to package instructions until tender. Drain and set aside.
Prepare the Sauce: In a small bowl, mix the soy sauce, hoisin sauce, and cornstarch-water mixture. Set aside.
Cook the Chicken: Season the chicken with salt and pepper. Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the sliced chicken and cook for about 5 - 7 minutes, or until fully cooked to an internal temperature of 160°F (71°C). Remove the chicken from the skillet and set aside.
Stir-fry the Vegetables: In the same skillet, add a little more oil if needed. Add the garlic and ginger, and cook for about 30 seconds until fragrant. Add the broccoli, carrots, and snap peas. Stir-fry for about 3 - 4 minutes until the vegetables are tender-crisp.
Combine and Finish: Return the chicken to the skillet. Pour in the prepared sauce and toss everything together to coat. Cook for an additional 2 - 3 minutes until the sauce thickens and everything is heated through. Stir in the sesame oil and season with salt and pepper to taste. Garnish with scallions and sesame seeds.
Serve the stir fry with coconut water.