Preheat a large skillet or wok to medium heat. Add vegetable oil, 1 Tablespoon sesame oil and shrimp to the skillet and salt and pepper. Cook the shrimp for 2-3 minutes or until no longer pink. Remove with a slotted spoon and set aside.
Add white onion and peas and carrots and fry until tender. Slide the onion, peas and carrots to the side, and pour the beaten eggs onto the other side. Using a spatula, scramble the eggs. Once cooked, mix the eggs with the vegetable mix.
Add the rice and shrimp to the veggie and egg mixture. Pour the soy sauce and 1 Tablespoons sesame oil on top. Stir and fry the rice and veggie mixture until heated through and combined. Add chopped green onions if desired.