Turn oven to broil (high) and place rack 8" below heating element. Slice the chicken breast into thick strips. Combine the sake, ginger, miso and salt. Toss the chicken strips into the mixture. Place chicken on a baking pan. Broil for 8 minutes or until chicken is cooked through.
In the meantime, add the sesame seeds to a frying pan and roast over medium-high heat while shaking the pan to avoid burning the seeds. When the seeds start to pop, remove from the heat.
Reserve 1 teaspoon of the toasted seeds and set aside.
For the dressing, slide the remaining seeds into a Japanese grinding bowl or mortar and grind roughly. Mash in the miso to form a thick paste and add the vinegar to lighten (and brighten) the miso-sesame mixture. Whisk in the oil slowly until emulsified. (Be sure to whisk again right before dressing your salad.)
Toss the lettuce with the dressing. Place the chicken on top of the lettuce and sprinkle with the reserved toasted sesame seeds. Serve immediately.