In a small bowl, mix together the soy sauce, sherry, sugar, and cornstarch.
In a large skillet or a wok, heat 2 tablespoons of the oil over high heat, and add half the ginger. Stir for 1 minute until you can smell the ginger, then add half the scallions and the chicken and sauté for about 3 minutes until the chicken is mostly white on the outside but still slightly raw inside and the scallions have started to soften. Remove the chicken and scallions from the skillet to a serving bowl and set aside.
Repeat with the remaining oil, ginger, scallions, and chicken. When the chicken is mostly cooked out the outside, return the first batch of cooked chicken and scallions to the pan, along with any juices that have accumulated, and add the soy sauce mixture. Stir to coat the chicken with the mixture. Add the chicken broth and sesame oil, bring to a simmer, and allow the sauce to thicken while the chicken finishes cooking, about 3 minutes more.
Serve hot, sprinkled with the sesame seeds if desired.
Notes
You can cut up all of the ingredients up to 3 days ahead of time and store them separately in the fridge.
You can make the sauce up to 4 days ahead of time and keep it in a container in the refrigerator.
Leftovers will last for 3 days in the fridge. Reheat leftovers in the microwave just until warmed through. You can also reheat them over medium heat in a wok or skillet on the stove.
Use either chicken breasts or thighs. Thighs will need an extra few minutes to cook through.
If you have a really big industrial-sized wok, you could do this in one batch, but the secret to great stir-fries (and lots of other cooking methods, like frying and sautéing) is to not crowd the pan. Giving the individual pieces of food a chance to come into direct contact with the hot pan on a continuous basis is the difference between nicely browned pieces and a pile of steamed food.
So, cook it in two batches: the cooking process is super quick, made quicker when the batches of food are small, so it only takes a handful of extra minutes.