Pat the chicken breast cubes dry with paper towels to ensure a better sear, then toss them in a bowl with arrowroot starch, sea salt, and black pepper until evenly coated.
Heat the avocado oil in a large skillet over medium-high heat. Once shimmering, add the chicken in a single layer and cook for 5-6 minutes, turning occasionally until golden brown and crispy.
While the chicken cooks, steam the broccoli florets for 3-4 minutes until they are bright green and crisp-tender.
In a small glass jar or bowl, whisk together the tamari, honey, minced ginger, minced garlic, and toasted sesame oil to create the glaze.
Reduce the skillet heat to medium, add the steamed broccoli and the sauce mixture to the chicken, and toss continuously for 1-2 minutes until the sauce thickens and coats everything beautifully.
Divide the cooked brown rice into bowls, top with the sesame chicken and broccoli mixture, and garnish with sesame seeds before serving.