Cut the chicken breast into bite-sized pieces and place them in a bowl. Toss with arrowroot starch, sea salt, and black pepper until evenly coated.
In a small jar or bowl, whisk together the honey, tamari, minced garlic, and grated fresh ginger to create the stir-fry sauce.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat.
Add the chicken pieces to the hot skillet in a single layer. Cook for 3-4 minutes per side until they are golden brown and cooked through.
Remove the chicken from the pan and set aside. In the same pan, add the broccoli, sliced bell pepper, and snap peas with a splash of water. Cover and steam for 2 minutes.
Remove the lid and return the chicken to the pan. Pour the honey-garlic sauce over the mixture and toss constantly for 1-2 minutes until the sauce thickens and becomes sticky.
Serve the hot stir-fry over the cooked brown rice immediately.