Heat the avocado oil in a large cast-iron skillet or wok over medium-high heat.
Season the diced chicken breast with sea salt and black pepper, then add it to the skillet, searing until golden brown and cooked through.
Remove the chicken from the pan and set it aside on a clean plate.
Lower the heat to medium and add the toasted sesame oil to the same skillet.
Add the diced carrots, minced garlic, and grated ginger, sautéing for 2-3 minutes until the vegetables are tender-crisp and fragrant.
Push the vegetable mixture to the sides of the skillet and crack the egg into the center, scrambling it quickly until fully set.
Stir in the cooked brown rice, frozen peas, and tamari, tossing everything together to combine.
Return the cooked chicken to the skillet and stir-fry for an additional 2 minutes until the rice is slightly crispy and the dish is heated through.
Remove from heat and garnish with freshly sliced green onions before serving.