In a small bowl, whisk together eggs and the water. Coat an unheated 12-inch nonstick skillet with cooking spray. Preheat skillet over medium heat. Pour in egg mixture. Cook, without stirring, until mixture begins to set on the bottom and around edges. With a spatula or large spoon, lift and fold the partially cooked eggs so that the uncooked portion flows underneath. Continue cooking over medium heat for 2 to 3 minutes or until egg mixture is cooked through, but is still glossy and moist, keeping eggs in large pieces. Carefully transfer eggs to a medium bowl; set aside.
In the same skillet, heat oil over medium-high heat. Add ginger and garlic; cook for 30 seconds. Add cabbage, carrot, and pea pods; cook and stir for 2 minutes. Stir in cooked eggs, brown rice, green onion, soy sauce, and chile sauce; cook and stir about 2 minutes or until heated through. Top with cilantro. Serve with lime slices.