In a large bowl, combine soy sauce, water, mirin, sake, brown sugar, granulated sugar, garlic, scallion whites, and ginger. Store half the teriyaki sauce mixture in a sealed container in the refrigerator. Combine chicken in bowl with the remainder of the teriyaki sauce mixture and marinate in the refrigerator for 30 minutes.

Heat a wok or medium skillet on medium-high heat until it is almost smoking. Add oil. When oil is hot, add garlic and crushed red pepper. Stir-fry for 30 seconds.

Add chicken. Let brown briefly, then stir-fry, moving the chicken around the pan until it turns white and is nearly cooked—about 3 to 4 minutes.

Add reserved marinade into pan. Reduce heat and cook, stirring occasionally for an additional 2 minutes or until chicken is fully cooked and nicely glazed with sauce. Serve hot over rice, garnishing with scallion greens.