Cut the chicken breast into bite-sized 1-inch pieces and season evenly with sea salt and black pepper.
Finely mince the garlic cloves and grate the fresh ginger using a microplane.
Heat the avocado oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the chicken pieces to the skillet in a single layer and sear until golden brown and cooked through, approximately 5 to 6 minutes.
Remove the cooked chicken from the pan and set it aside on a clean plate.
In the same skillet, add the toasted sesame oil followed by the broccoli florets and sliced red bell pepper.
Stir-fry the vegetables for 3 to 4 minutes until they are tender-crisp and the colors are bright.
Stir in the minced garlic and grated ginger, sautéing for only 30 seconds until highly fragrant to avoid burning.
Return the chicken and any accumulated juices to the pan and pour in the coconut aminos.
Toss all ingredients together for 1 minute to ensure the sauce coats everything evenly.
Serve the stir-fry immediately over the warm cooked brown rice and garnish with a sprinkle of sesame seeds.