Pat the chicken breast dry and cut into 1-inch bite-sized pieces.
In a small bowl, toss the chicken with arrowroot powder, sea salt, and black pepper until evenly coated.
Whisk together the honey, tamari, minced garlic, and grated ginger in a separate small bowl to create the sauce.
Heat the sesame oil in a large skillet or wok over medium-high heat.
Add the chicken to the skillet and cook for 5-6 minutes, turning occasionally until golden brown and cooked through.
Remove the chicken from the pan and set aside; add the broccoli and sliced bell peppers to the same pan with a splash of water.
Steam-sauté the vegetables for 3-4 minutes until they reach a vibrant green and crisp-tender texture.
Return the chicken to the skillet and pour the honey-garlic sauce over the mixture.
Toss everything together for 1-2 minutes until the sauce thickens and glazes the chicken and vegetables.
Serve the stir-fry immediately over the warm cooked brown rice.