Coat beef strips in cornstarch and place on a plate. Let stand for about 5-10 minutes.
Slice the green onions and set aside.
Heat the sesame oil in a wok or frying pan, over medium heat, being careful not to let it get too hot. Add the garlic and ginger and saute for about 1 minute, being careful not to let it burn. Then add the soy sauce, water and brown sugar, stirring until sugar is dissolved. Remove from heat and set aside.
Heat about 2 inches of oil in a wide pot over medium heat. Add the beef in one layer and fry until browned, about 2-3 minutes. Carefully remove the beef slices with a slotted spoon and let them drain on a paper towel.
Put the wok or pan with the sauce back over medium heat and add the beef strips and bring to a simmer. Add the green onions, simmer for another minute or so. Serve over rice.