Heat 2 tablespoons peanut oil in a large wok or nonstick skillet over high heat. Meanwhile, crack the eggs into a small bowl along with 1/2 teaspoon of salt, and beat with a fork or whisk until well mixed.
Pour the egg into the warm wok or skillet and cook, stirring constantly with a spatula, for 5 or 6 minutes, until the egg is broken up into small pieces and is crispy and golden. Remove the egg from the pan and set aside for later.
Add the remaining 2 tablespoons peanut oil to the wok or skillet and keep the heat on high. Add the rice and green onion and stir fry for about 10 minutes until the green onion is cooked.
Next add the peas and carrots, chicken broth, remaining 1/2 teaspoon of salt, and soy sauce and continue to cook for about 5 minutes until hot and well mixed. Add the cooked egg, ground black pepper, and sesame oil, stir to mix well, and remove from heat. Enjoy while hot. (Although it makes great leftovers too!)