Crack the eggs into a bowl and add a splash of water. Beat with a whisk until combined.
Lightly mist a large saute pan with cooking spray and bring to medium heat. Pour in the beaten eggs and cook, stirring continuously, to form large curds. When the eggs are scrambled, remove them to a side plate and set aside. Wipe out the pan with a paper towel to use in the next step.
Add 2 teaspoons of the sesame oil to the pan and bring to medium heat. Add the onions and carrots and stir to coat. Cook, stirring occasionally, for 5-7 minutes until the vegetables are softened. Add the garlic and cook for an additional 30-60 seconds until fragrant.
Add the cold rice and peas and stir together. Cook for 3-4 minutes, stirring occasionally.
In a separate dish, stir together the soy sauce, oyster sauce, ground ginger, and the remaining teaspoon of sesame oil. Pour this sauce over the rice in the pan and then stir until the rice is coated. Add the scrambled eggs to the pan as well. Cook for another 1-3 minutes, stirring occasionally, until heated through. Sesaon with salt and pepper to taste if desired.