Using a sharp knife, begin by cutting off and discarding any thick stems from the broccoli and then cut the broccoli into thin, long florets.
Dry saute the sesame seeds over medium heat in a small frying pan until they are toasted. Be careful not to leave them unattended when toasting, as they will readily burn if left on for even a fraction too long.
After heating the olive oil in a large frying pan or wok, stir-fry the broccoli for 3 to 4 minutes, or until tender. If the pan becomes too dry, add a splash of water to the broccoli.
Add the soy sauce to the broccoli, and season it with salt and freshly ground black pepper.
Toss in the sesame seeds and then serve immediately.