Place cornstarch on a shallow plate.
Dip steak slices into the cornstarch, applying it on both sides of each slice of beef.
Let stand for 10 minutes, while you work on the sauce.
In a saucepan, heat 2 teaspoons vegetable oil over medium-low heat.
Add ginger and garlic to the pan; cook for 10 seconds, or until fragrant.
Stir in soy sauce and water.
Whisk in brown sugar; cook while stirring until sugar dissolves.
Set to medium heat and cook the sauce until it thickens; about 10 minutes.
Remove from heat and set aside.
Place vegetable oil in a separate large saucepan and heat over medium heat until hot.
Add previously prepared steak slices to the oil and cook for 2 to 3 minutes, or until cooked through, flipping the pieces over to cook on the opposite side.
Remove meat from oil and drain on paper towels.
Return saucepan to stove and heat over medium heat.
Add steak slices and cook for 1 minute.
Gently stir in previously prepared sauce; continue to cook and stir for a minute.
Stir in green onions and cook for 1 to 2 minutes, or until heated through.
Remove from heat.
Serve over white rice.