Heat the oil in a wide skillet over medium-high heat. Once the oil is shimmering, add the garlic, ginger, and onions and cook until onions are soft, 3-5 minutes. Add the brussels sprouts, season with pepper and cook until sprouts are bright green and wilted. Add in the chicken and brown rice and stir well to combine. Create a cavity in the center of the rice mixture and pour in the eggs. Scramble, stirring often. Once eggs are scrambled, stir to combine the mixture. Add in the soy sauce, stir again, season with more pepper, and serve.