Pat the chicken breast dry with a paper towel and cut into bite-sized 1-inch cubes.
Season the chicken cubes evenly with the sea salt and black pepper.
In a small glass bowl, whisk together the tamari, toasted sesame oil, grated fresh ginger, and minced garlic 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 in a single layer and sear for 3-4 minutes until golden brown and cooked through.
Toss in the broccoli florets and add a splash of water, covering the pan for 2 minutes to lightly steam the broccoli until it is bright green and tender-crisp.
Remove the lid, pour the prepared sesame-ginger sauce over the chicken and broccoli, and toss for 1 minute until the sauce thickens and coats everything beautifully.
Serve the stir-fry immediately over the warm cooked brown rice and garnish with the sesame seeds.