Pat the chicken breast dry with a paper towel and cut into 1-inch bite-sized pieces, then season evenly with sea salt and black pepper.
In a small glass bowl, whisk together the coconut aminos, rice vinegar, honey, minced fresh ginger, minced garlic, red pepper flakes, and arrowroot powder until no lumps remain.
Heat the avocado oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the chicken pieces to the skillet in a single layer and sear for 3-4 minutes per side until they are golden brown and fully cooked through.
Remove the chicken from the skillet and set aside on a plate; add the broccoli florets and 1 tablespoon of water to the same skillet.
Cover the skillet immediately with a lid and steam the broccoli for 2 minutes until it is bright green and tender-crisp.
Remove the lid, return the chicken to the pan, and pour the prepared sauce mixture over the chicken and broccoli.
Toss everything together for 1-2 minutes until the sauce thickens into a glossy glaze that coats every piece.
Remove from heat, drizzle with toasted sesame oil, and serve immediately over the warm cooked brown rice.