Pat chicken breast pieces 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 stainless steel skillet or wok over medium-high heat until shimmering.
Add the chicken to the pan in a single layer and sear for 3-4 minutes per side until golden brown and cooked through, then transfer to a plate.
In the same skillet, add the broccoli and bell peppers with a tablespoon of water; cover and steam for 2 minutes until tender but still crisp.
While vegetables cook, whisk together the orange juice, tamari, honey, grated ginger, and minced garlic in a small bowl.
Return the chicken to the skillet, pour the orange sauce over the top, and simmer for 1-2 minutes until the glaze thickens and coats the ingredients.
Remove from heat, stir in the toasted sesame oil, and serve immediately over warm brown rice garnished with sesame seeds.