In a small bowl, whisk together the cornstarch with the soy sauce, brown sugar, garlic and ginger. Set the sauce aside.
Heat a large wok or skillet over high heat. Add 1 tablespoon vegetable oil and heat until it begins to smoke. Add the beef and cook until completely browned, stirring frequently, about 3-4 minutes. Add the remaining oil and them the broccoli and onions. Cook for 2-3 minutes, stirring frequently, until the broccoli is vibrant green and slightly tender.
Add the sauce and reduce the heat to medium. Cook for one minute after sauce boils. Remove from heat and serve over cooked rice.