Pat the chicken breast dry with paper towels and cut into 1-inch bite-sized cubes.
Season the chicken cubes evenly with the sea salt and black pepper.
Heat the avocado oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the chicken to the pan in a single layer and sear for 5-6 minutes, turning occasionally, until golden brown and cooked through.
Remove the cooked chicken from the pan and set it aside on a clean plate.
Add the broccoli florets and sliced red bell pepper to the same pan, sautéing for 3-4 minutes until they are tender-crisp.
Stir in the minced garlic and grated fresh ginger, cooking for about 30 seconds until the mixture becomes highly fragrant.
Return the chicken to the pan and pour in the coconut aminos and toasted sesame oil.
Toss all ingredients together for 1 minute to ensure everything is well-coated and the sauce has slightly thickened.
Serve the hot stir-fry over the warm cooked brown rice and garnish with sesame seeds before serving.