In a small bowl, whisk together the coconut aminos, honey, minced ginger, minced garlic, arrowroot powder, and water until the mixture is smooth.
Season the diced chicken breast evenly with the sea salt and black pepper.
Heat the sesame oil in a large skillet or wok over medium-high heat until shimmering.
Add the chicken to the skillet and sauté until golden brown and cooked through, approximately 5 to 7 minutes.
Add the broccoli florets to the pan with a small splash of water, then cover with a lid to steam for 2 minutes until tender-crisp.
Remove the lid and pour the prepared sauce over the chicken and broccoli, stirring constantly for 1 minute until the glaze thickens and looks glossy.
Transfer the stir-fry to a plate and serve immediately over the warm, fluffy brown rice.