Heat one tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Pour in the beaten eggs and scramble them until they are just cooked through. Break them into small pieces with your spatula, remove them from the pan, and set them aside.

Wipe the skillet clean if necessary and add the remaining tablespoon of oil. Increase the heat to high. Add the diced onion and the peas and carrots. Sauté for about 2 to 3 minutes until the onions are translucent. Stir in the minced garlic and cook for another 30 seconds until fragrant.

Add the chilled cooked rice to the skillet. Use your spatula to break up any large clumps. Fry the rice for 3 to 4 minutes, stirring frequently, until the rice starts to brown slightly and picks up a toasted aroma.

Pour the soy sauce and toasted sesame oil over the rice. Sprinkle with black pepper. Toss everything together so the rice is evenly coated in the sauce. Fold the cooked eggs and sliced green onions back into the mixture.

Give everything one final toss on high heat for about 1 minute. Taste and add more soy sauce if desired. Remove from heat immediately to prevent the rice from drying out.