Make the sauce by stirring together one-third cup of water, the oyster sauce, chili oil, salt, sugar, starch and sesame seed oil. Set aside.
Pre-cook the broccoli. Boil about four cups of water in a pan. Throw in the broccoli florets. When the water boils once more, turn off the heat and scoop out the broccoli. Dump the florets into a bowl of iced water. Stir a little, let them get really cold then drain.
Set the heat on low and pour the cooking oil in a wok. Add the garlic and ginger. Cook gently for a couple of minutes to allow them to flavor the oil.
Turn up the heat. When the oil is smoking, add the shrimps. Stir fry just until the shrimps change color. Add the broccoli. Pour in the sauce. Stir until the sauce thickens and is no longer cloudy.
Tip the contents of the wok onto a serving platter and serve the shrimp and broccoli stir fry immediately.