Slice the chicken breast into thin, bite-sized strips and season evenly with sea salt and black pepper.
In a small glass bowl, whisk together the coconut aminos, toasted sesame oil, and arrowroot powder until the powder is fully dissolved to create your stir-fry sauce.
Heat the avocado oil in a large cast-iron skillet or wok over medium-high heat until it begins to shimmer.
Add the chicken strips to the skillet in a single layer and sear for 5-6 minutes, turning occasionally, until golden brown and cooked through.
Transfer the cooked chicken to a plate and add the broccoli florets to the same skillet with two tablespoons of water; cover with a lid for 2 minutes to steam until bright green.
Remove the lid and add the minced garlic and grated ginger to the broccoli, sautéing for 60 seconds until highly fragrant.
Return the chicken to the skillet and pour the prepared sauce over the mixture, tossing constantly for 1-2 minutes until the sauce thickens into a glossy glaze.
Garnish with sesame seeds and serve immediately while hot.