Pat the chicken breast completely dry with paper towels and cut into bite-sized cubes.
In a small bowl, whisk together the coconut aminos, minced ginger, and minced garlic to create the clean teriyaki base.
Toss the chicken cubes in a separate bowl with arrowroot starch, sea salt, and black pepper until evenly coated.
Heat the avocado oil in a large non-stick skillet over medium-high heat until shimmering.
Add the chicken to the skillet in a single layer and sear for 5-6 minutes, turning occasionally until golden brown and crispy.
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 for 2 minutes to steam the broccoli until it is bright green and crisp-tender.
Remove the lid, return the chicken to the pan, and pour the coconut aminos mixture over the top.
Stir constantly for 1-2 minutes until the sauce thickens into a glossy glaze that coats the chicken and broccoli.
Remove from heat, drizzle with toasted sesame oil, and serve immediately over the warm cooked brown rice.