Dice the chicken breast into small, bite-sized pieces and season with black pepper.
Heat the avocado oil in a large skillet or wok over medium-high heat until shimmering.
Add the chicken to the skillet and sauté until golden brown and cooked through, approximately 5-6 minutes.
Mince the garlic and grate the ginger, then add them to the skillet, stirring for 30 seconds until fragrant.
Add the chopped kimchi to the pan and cook for 2 minutes, allowing it to slightly caramelize and release its juices.
Incorporate the cooked brown rice and tamari into the mixture, using a spatula to break up any clumps and ensuring the rice is evenly coated and heated.
Stir in the sesame oil and half of the sliced green onions, then remove the skillet from the heat.
In a separate small non-stick pan, fry the egg over medium heat until the whites are set but the yolk remains runny.
Transfer the kimchi fried rice to a bowl, top with the fried egg, and garnish with the remaining green onions.