Whisk scallions, minced garlic, minced ginger, 1 cup water, 6 tablespoons soy sauce, 6 tablespoons sugar, and cornstarch together in a large bowl. Add beef; mix gently to coat. Cover with plastic wrap and refrigerate for 1 hour.
Whisk 1 1/3 cups water, 1/2 cup sugar, and 1/2 cup plus 2 tablespoons soy sauce in a bowl to make the sauce.
Spray a large skillet with cooking spray; warm over medium-high heat. Whisk eggs together in a bowl. Pour into the skillet; cook and stir until eggs are set, about 5 minutes. Transfer scrambled eggs to a bowl.
Heat sesame oil in the same skillet over medium-high heat. Add diced garlic and diced ginger. Saute until golden brown and fragrant, about 2 minutes. Add carrots and onion; saute until carrots are tender and onions are translucent, about 5 minutes.
Strain beef from marinade and add to skillet. Cook and stir until beef can be easily pulled apart with a fork, 5 to 7 minutes.
Stir in bean sprouts; cook until translucent, about 1 minute. Add corn and peas; cook and stir until heated through, about 2 minutes. Create a pocket in the center of the skillet and slowly add rice, stirring to incorporate, about 1 minute. Add sauce and stir until rice is evenly coated, about 1 minute. Add scrambled eggs, stir and let heat through, about 1 minute.