Prepare noodles according to package directions, drain, and set aside.
In a small mixing bowl, whisk together the soy sauce, chili garlic sauce, honey, and sesame oil to create the glaze.
Heat vegetable oil in a large wok or skillet over medium-high heat until shimmering.
Add chicken cubes to the skillet and sear until golden brown and cooked through, approximately 6 to 8 minutes.
Stir in the minced garlic and grated ginger, cooking for 60 seconds until fragrant.
Add broccoli florets and 2 tablespoons of water; cover the pan for 2 to 3 minutes to steam the broccoli until tender-crisp.
Remove the lid and pour the prepared glaze over the chicken and broccoli, stirring constantly for 1 minute to thicken.
Add the cooked noodles to the skillet and toss thoroughly to ensure even coating in the sauce.
Garnish with sliced green onions and toasted sesame seeds before portioning into bowls.