Start with rice that has been cooked and chilled—warm rice will lend a soggy texture to fried rice.
Beat the eggs in a small bowl and set them aside.
Heat oil in a wok or frying pan over medium heat.
Add rice and cook, stirring, for a few minutes or until rice begins to brown. If rice sticks to the pan, add more cooking oil.
Add the shrimp and sesame oil to the rice. Fry, stirring occasionally until shrimp are pink.
Chop the onion and add to the rice. Then add the carrot.
Add the soy sauce and pepper to taste. Cook, stirring, for 5 to 10 minutes or until the carrots are tender.
Add the beaten eggs and cook, stirring, for a minute or two.
Serving Suggestions: Serve with lemon and sliced scallions.