Dice the chicken breast into small, uniform bite-sized pieces and season evenly with 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 skillet and cook undisturbed for 3 minutes to develop a golden crust, then toss and cook for another 3 minutes until fully cooked through.
Push the chicken to the outer edges of the pan and add the toasted sesame oil to the center.
Stir in the diced carrots, frozen peas, grated ginger, and minced garlic, sautéing for 2 minutes until fragrant and tender-crisp.
Add the cooked brown rice and cauliflower rice to the pan, pressing them down firmly with a spatula to allow the grains to crisp up for 2-3 minutes.
Create a small well in the center of the mixture, crack the egg into it, and scramble gently until just set before folding it into the rice and chicken.
Drizzle the coconut aminos over the entire dish and toss well to coat every ingredient in the savory sauce.
Garnish the fried rice with thinly sliced green onions and sesame seeds before serving immediately.