Heat one tablespoon of the vegetable oil in a large high sided frying pan on a medium-high heat. Add the shrimp, season with some salt and pepper to taste and fry for a couple of minutes on each side until pink all over and cooked through. Remove from the pan and set aside.
Reduce the heat to medium and add the eggs to the pan. Stir rapidly with a wooden spoon as they cook to scramble them. This should take about 2 minutes. Remove from the pan and set aside.
Add the second tablespoon of vegetable oil to the pan. Add the onion, the white parts of the green onions, the carrot and pepper. Fry for about 6-8 minutes until softened, stirring frequently. Add the garlic and ginger and fry for another minute.
Add the peas, stir well and cook for 2 minutes.
Add the rice and let it warm through for another few minutes, breaking any clumps apart with a wooden spoon as it cooks.
Add the shrimp and egg back to the pan. Then pour over the sesame oil and soy sauce. Stir and let everything cook for a final couple of minutes.