Preheat oven to 350°, rack in the middle position. In a medium skillet over medium heat, heat 2 tablespoons neutral oil. Season chicken with salt and pepper on both sides, then add to skillet. Cook until golden on both sides, 8 minutes per side.  Transfer pan to oven and bake until cooked through, 6-8 minutes longer. Remove from skillet and let rest 5 minutes, then cut into bite-sized pieces. To the same skillet, heat 2 tablespoons oil. Add onion and carrots and cook until soft, 5 minutes, Add garlic and ginger and cook until fragrant, 1 minute more. Stir in rice and peas and cook until warmed through, 2 minutes. Push rice to one side of skillet and add remaining tablespoon oil to other side. Add egg and stir until almost fully cooked, then fold eggs into rice. Add chicken back to skillet with soy sauce and green onions and stir to combine.