Whisk eggs in a small bowl, and set aside. Then, in a separate bowl, combine soy sauce and sesame oil. Chop green onions, separating the white and green parts.

Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the beaten eggs and scramble until fully cooked. Remove the eggs and set aside. Add the remaining vegetable oil to the skillet. Then add shrimp and cook until pink and opaque, about 2-3 minutes per side. Remove shrimp from the skillet and set aside. Add minced garlic and grated ginger to the skillet and stir-fry for 30 seconds until fragrant. Add the day-old rice and frozen peas and carrots to the skillet. Break up any clumps of rice and stir-fry for 3-5 minutes, ensuring the rice is heated through and slightly crispy. Add the cooked shrimp, scrambled eggs, and the white parts of the green onions to the skillet. Pour the soy sauce and sesame oil mixture over the rice and ingredients. Stir-fry for another 1-2 minutes, mixing everything evenly. Stir in the green parts of the green onions just before serving.