Heat 1/2 tablespoon of butter in a large sauté pan over medium-high heat until melted. Add egg, and cook until scrambled, stirring occasionally. Remove egg, and transfer to a separate plate.Add an additional 1 tablespoon butter to the pan and heat until melted. Add carrots, onion, peas and garlic, and season with a generous pinch of salt and pepper. Sauté for about 5 minutes or until the onion and carrots are soft. Increase heat to high, add in the remaining 1 1/2 tablespoons of butter, and stir until melted. Immediately add the rice, green onions, soy sauce and oyster sauce (if using), and stir until combined. Continue stirring for an additional 3 minutes to fry the rice. Then add in the eggs and stir to combine. Remove from heat, and stir in the sesame oil until combined.Serve immediately, or refrigerate in a sealed container for up to 3 days.