In a small glass bowl, whisk together the coconut aminos, honey, fresh ginger, garlic, and water until well combined.
Pat the chicken breast dry with a paper towel, then season evenly with sea salt and black pepper.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the chicken to the hot skillet in a single layer, searing until golden brown and fully cooked, about 6 minutes.
Toss in the broccoli florets with a tablespoon of water, then immediately cover with a lid to steam for 2 minutes until bright green.
Remove the lid and pour the sauce over the mixture, stirring constantly as it bubbles and thickens into a glossy glaze.
Divide the warm brown rice into bowls, top with the chicken and broccoli, and finish with a sprinkle of sesame seeds.