Pat the chicken breast dry with a paper towel and toss in a bowl with arrowroot powder, sea salt, and black pepper until evenly coated.
Heat avocado oil in a large skillet over medium-high heat until shimmering.
Add the chicken to the skillet in a single layer and cook until golden brown and crispy on all sides, approximately 6 to 8 minutes.
Remove the chicken from the pan and set aside; add the broccoli florets and 2 tablespoons of water to the same pan.
Cover the pan with a lid and steam the broccoli for 3 minutes until tender-crisp and bright green.
In a small bowl, whisk together the coconut aminos, honey, toasted sesame oil, minced ginger, and minced garlic.
Return the chicken to the skillet with the broccoli and pour the sauce mixture over the top.
Sauté for 1 to 2 minutes, tossing constantly, until the sauce thickens into a glossy glaze that coats the chicken and vegetables.
Serve the mixture immediately over the warm cooked brown rice and garnish with sesame seeds.