Rinse the Japanese Short-Grain Rice under cold water until the rinse water runs mostly clear; drain, then add to a pot with fresh water (or a rice cooker) and soak for 20–30 minutes if you have time. Cook according to your pot or rice-cooker instructions and keep warm.
Whisk together the Soy Sauce, Mirin, Sake and Sugar in a small bowl until the sugar is mostly dissolved to make the teriyaki sauce. Set aside.
Pat the Chicken Thighs dry with paper towels and, if they have skin, score the skin lightly in a crosshatch so they render and crisp evenly.
Heat a large skillet over medium-high heat and add the Neutral Oil. When the oil is shimmering, place the thighs skin-side down and cook without moving until the skin is well browned and crisp, about 6–8 minutes. Flip and cook the other side 3–5 minutes until nearly cooked through.
Pour the prepared teriyaki sauce into the pan with the chicken and reduce the heat to medium-low. Simmer gently, spooning the bubbling sauce over the thighs, until it thickens into a glossy glaze and the chicken is cooked through, about 3–5 minutes. Tilt the pan and spoon the reduced sauce over the meat as it cooks.
Transfer the chicken to a cutting board and let rest 3–5 minutes, then slice or chop into serving pieces. Return the chicken briefly to the pan and toss in the remaining glaze to coat if desired.
Thinly slice the Green Cabbage and either toss it raw as a crisp bed for the chicken or quick-sauté it in the same skillet for 1–2 minutes to wilt slightly and pick up any flavorful browned bits.
Serve the glazed chicken over the warm rice with the cabbage alongside, and spoon any extra teriyaki glaze from the pan over the chicken and rice for maximum flavor.
