If using frozen broccoli, steam cook in a pot with lid on for about 2 minutes with 2 tablespoons (EL) water. If using fresh broccoli, simply chop into small florets.
Mix the broth, soy sauce, and half tablespoon (1/2 EL) oil. Set aside.
Heat remaining 1/2 tablespoon oil in a pan. Add the broccoli, stir to coat with the oil, and sauté for about a minute. Add the ginger and garlic. Add bowl with broth, soy sauce, and oil and bring to a simmer. Cook until the liquid is almost gone. Mix in sesame seeds.