Thinly slice the flank steak against the grain into strips, about 1/4 inch thick. Pat the beef dry with paper towels.

In a medium bowl, toss the sliced steak with cornstarch until each piece is evenly coated. Set aside.

In a separate small bowl, whisk together the soy sauce, water, brown sugar, grated fresh ginger, minced garlic, sesame oil, and red pepper flakes (if using) to create the Mongolian sauce. Set aside.

Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add half of the cornstarch-coated beef in a single layer, ensuring not to overcrowd the pan. Cook for 2-3 minutes per side until browned and slightly crispy. Remove the cooked beef from the skillet and set aside on a plate.

Add the remaining 1 tablespoon of vegetable oil to the skillet and cook the second batch of beef in the same manner. Remove and add to the first batch.

Pour the prepared Mongolian sauce into the empty skillet. Bring the sauce to a simmer, stirring occasionally, and let it cook for 2-3 minutes, or until it has slightly thickened to a glaze-like consistency.

Return all the cooked beef to the skillet and toss to coat it evenly with the sauce. Continue to cook for another 1-2 minutes, stirring constantly, until the beef is heated through and thoroughly coated in the sauce.

Garnish the Mongolian Beef with freshly sliced green onions and serve immediately over hot steamed rice or noodles.