Place cornstarch on a shallow plate. Dip steak slices into the cornstarch, applying it on both sides of each slice of beef. Put the steak pieces aside for 10 minutes while you work on the sauce.

In a saucepan, heat 2 teaspoons of vegetable oil over medium-low heat. Add ginger and garlic to the pan; cook for 10 seconds or until fragrant.

Stir in the soy sauce and water. Whisk in brown sugar and cook while stirring until the 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 skillet and heat over medium heat until hot. Add the 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.

Using tongs, remove the steak pieces from the oil and let them drain on paper towels.

Discard the oil. Return the saucepan to the stove and heat over medium heat. Add steak slices and cook for 1 minute. Gently stir in the 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 and serve over rice.