Pierce the chicken skin in several places with a fork. If the chicken meat is uneven in thickness, slice it open to even it out.
Mix the teriyaki sauce ingredients (sake, mirin, sugar, and soy sauce) in a bowl.
Heat oil in a pan. Sauté the chicken over medium heat, starting with the skin side down, until golden brown. Occasionally press the chicken with a spatula to ensure even browning.
Flip the chicken over, cover the pan, and let it cook over medium heat for about 3 minutes.
Turn off the heat, remove the lid, and wipe off any excess fat from the pan with paper towels. Then, add the teriyaki sauce from the bowl and cook over medium heat again, turning the chicken occasionally, until the sauce is almost fully reduced.
Remove the chicken and cut it into ⅘-inch (2cm) pieces.
Serve the chicken pieces on plates and drizzle with any sauce remaining in the pan. Garnish with a lettuce and cherry tomatoes on the side, if desired.