In a large bowl, whisk together 2 tablespoons cornstarch with 3 tablespoons water. Add the beef to the bowl and toss to combine.
In a separate small bowl, whisk together the remaining 1 tablespoon cornstarch with the soy sauce, brown sugar, garlic and ginger. Set the sauce aside.
Heat a large nonstick sauté pan over medium heat. Add 1 tablespoon of the vegetable oil and once it is hot, add the beef and cook, stirring constantly until the beef is almost cooked through. Using a slotted spoon, transfer the beef to a plate and set it aside.
Add the remaining 1 tablespoon of vegetable oil to the pan and once it is hot, add the broccoli florets and sliced onions and cook, stirring occasionally, until the broccoli is tender, about 4 minutes. (See Kelly’s Notes.)
Return the beef to the pan then add the prepared sauce. Bring the mixture to a boil and cook, stirring, for 1 minute or until the sauce thickens slightly. Serve with rice or noodles.