Combine 3 tablespoons soy sauce, the sesame oil, sugar, sambal oelek and grated garlic in a shallow baking dish. Add the chicken and toss to coat; set aside while you fry the garlic and make the rice.
Meanwhile, heat 2 tablespoons vegetable oil in a large nonstick skillet over medium heat. Add the sliced garlic and cook, stirring, until golden and crisp, 2 to 3 minutes. Remove the garlic with a slotted spoon to a plate, leaving the oil in the skillet.
Add the ginger to the skillet and cook over medium heat, stirring, until sizzling, about 20 seconds. Add the cabbage and a big pinch of salt. Cook, tossing, until lightly browned, 3 to 5 minutes. Add the rice and 1/2 teaspoon salt and cook, tossing occasionally, until toasted, 3 to 5 minutes. Stir in the remaining 2 teaspoons soy sauce and all but 2 tablespoons scallions; season with salt.
Heat another large nonstick skillet over medium heat. Remove the chicken from the marinade, add 1 tablespoon water to the marinade and reserve. Season the chicken lightly with salt. Add the remaining 1 tablespoon vegetable oil and the chicken to the skillet. Cook until browned, about 3 minutes per side, adding the marinade to the skillet during the last 30 seconds of cooking and spooning it over the chicken.
Divide the rice and chicken among plates. Top with the fried garlic and reserved 2 tablespoons scallions.