Cut the chicken breast into bite-sized pieces and season evenly with sea salt and black pepper.
In a small bowl, whisk together the tamari, water, arrowroot powder, and toasted sesame oil until smooth to create the stir-fry sauce.
Heat the avocado oil in a large skillet or wok over medium-high heat until shimmering.
Add the chicken to the skillet and cook for 5-6 minutes, stirring occasionally, until golden brown and cooked through.
Add the broccoli florets, minced garlic, and grated ginger to the pan with a small splash of water.
Cover the skillet with a lid for 2 minutes to steam the broccoli until it is tender-crisp and bright green.
Remove the lid, pour the prepared sauce over the chicken and broccoli, and toss constantly for 1 minute until the sauce thickens into a glossy glaze.