Pat the chicken breast dry and cut into bite-sized cubes, then season with sea salt and black pepper.
Heat the avocado oil in a large skillet over medium-high heat until shimmering.
Add the chicken to the pan and sear for 5-6 minutes, turning occasionally until golden brown and cooked through.
Remove the chicken from the pan and set aside; add the broccoli florets to the same pan with a tablespoon of water.
Cover the pan with a lid for 2-3 minutes to steam the broccoli until tender-crisp and bright green.
In a small bowl, whisk together the coconut aminos, toasted sesame oil, grated ginger, and minced garlic.
Remove the lid, return the chicken to the pan, and pour the sauce over the chicken and broccoli.
Sauté for 1-2 minutes on high heat until the sauce reduces into a glossy glaze that coats everything.
Serve the mixture immediately over the warm brown rice and garnish with sesame seeds.