Bring the soy sauce and honey to a simmer in a small saucepan over medium heat, stirring often until the honey has completely dissolved, about 5 minutes. Add the ginger, stir to combine, remove from the heat, and set aside. If using chicken breasts, place them on a cutting board and cover with a sheet of plastic wrap. Use a meat mallet or a frying pan to gently pound them to a 1/2-inch thickness. Cut each in half so you have 4 pieces roughly the same size. (If using chicken thighs, no need to pound or cut.) Season both sides of the chicken with pepper. Heat the oil in a large frying pan over high heat until shimmering. Add the chicken in a single layer and cook without disturbing until browned, about 3 minutes. Flip and cook the second side until browned, about 3 minutes more. Reduce the heat to medium, slowly pour in the reserved sauce, and cook, flipping the chicken occasionally to coat in the sauce, until cooked through, about 3 minutes. Transfer the chicken from the pan, letting the excess sauce drip off, to a clean cutting board. Reduce the sauce in the pan over medium heat until slightly thickened, about 3 minutes more. Slice the chicken crosswise into 1/2-inch pieces. Place on a serving dish, top with the sauce, and sprinkle with the scallions.