First prepare the broccoli by cutting off the florets and dividing them into bite-sized pieces. Then chop the smaller stems into little chunks. Cut off and discard the bottom tough part of the broccoli stalk–about 1/2 to 1-inch, depending on the broccoli. Stand the stalk up on end and trim off the tough outer skin with a sharp knife (or just use a peeler). Slice the stalk into diagonal slices, about 1/8-inch thick.
Have about 1/2 cup of water ready by your stove. Using a wok or non-stick skillet that has a cover, put the sesame oil and 2 tablespoons of water into the pan, and heat it until it begins sizzling. Add the ginger and stir for 1 minute. Add the broccoli and, if the pan is dry, another 2 tbsp. of water. Stir quickly and cover. Cook for one minute.
Remove the cover and stir. Add another splash of water and cover again. Cook for one minute.
Repeat the process of stirring and adding a splash of water one more time. Check the broccoli, and if it is bright green yet becoming tender, it is done. If you want your broccoli more tender, repeat the process until it’s how you like it. When it’s done, add another tablespoon of water, the soy sauce, and the 1/4 teaspoon of sesame oil if you feel it needs more flavor. Toss well and serve immediately, sprinkled with sesame seeds.
Sesame oil has a lot of flavor in a tiny bit. You may be able to use less than I describe here and reduce the amount of fat and calories.