Cut the chicken breast into bite-sized pieces and season evenly with the sea salt and black pepper.
In a small mixing bowl, whisk together the tamari, honey, minced fresh ginger, minced garlic, and arrowroot powder to create the teriyaki base.
Heat the avocado oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the chicken pieces to the hot skillet and sear until they are golden brown and fully cooked, about 5 to 6 minutes.
Toss in the broccoli florets along with two tablespoons of water, then cover the pan with a lid for 2 minutes to steam them until tender-crisp.
Remove the lid and pour the prepared sauce over the chicken and broccoli, tossing continuously as the glaze bubbles and thickens.
Remove the skillet from the heat and drizzle the toasted sesame oil over the dish for a rich, nutty finish.
Garnish the stir-fry with sliced green onions and sesame seeds before serving hot.