Heat 1 tablespoon vegetable oil in a large skillet or wok over medium-high heat.
Add the shrimp to the skillet, season with 1/2 teaspoon salt and 1/4 teaspoon black pepper, and cook for 2-3 minutes until pink and opaque. Remove the shrimp from the skillet and set aside.
In the same skillet, pour in the beaten eggs and scramble until just set. Remove the eggs and set aside with the shrimp.
Add the diced onion and carrot to the skillet and sauté for 3-4 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the chilled cooked rice to the skillet and stir well to combine with the vegetables. Break up any clumps with the back of the spatula.
Pour in the soy sauce, oyster sauce, and toasted sesame oil. Stir thoroughly to evenly coat the rice and vegetables.
Return the cooked shrimp and scrambled eggs to the skillet. Stir everything together and cook for an additional 2 minutes to heat through.
Remove from heat and sprinkle the sliced green onions over the top.
Serve hot.