Slice the flank steak into thin ¼-inch pieces.
Toss the beef slices with cornstarch, shaking off any excess, and set aside.
In a 10-inch skillet, warm 2 teaspoons of oil over medium-low heat.
Add the minced ginger and garlic, and cook until fragrant (about 1 minute).
Stir in the soy sauce, water, and brown sugar. Bring the mixture to a boil and let it simmer for 3–5 minutes, or until slightly thickened.
Transfer the sauce to a small bowl and set aside.
In a separate pan or wok, heat 1 tablespoon of oil over medium-high heat.
Cook the beef in small batches for about 2 minutes per batch. The beef does not need to be fully cooked at this stage—just browned on the outside.
Once all the beef is browned, return it to the skillet.
Pour the reserved sauce over the beef and heat over medium heat until the mixture is hot and bubbly.
Remove the skillet from the heat and stir in the green onions.
Serve the beef and sauce over cooked rice.