Heat 2 teaspoons of oil in a large pan over medium high heat.
Place the ham in a single layer in the pan. Cook for 2-3 minutes, stirring occasionally, or until meat is browned.
Remove the ham from the pan. Place it on a plate. Cover the plate with foil to keep warm.
Pour 1 teaspoon of oil into the pan, then add the onion and carrots. Cook for 5-6 minutes or until the vegetables have softened. Season the vegetables with salt and pepper to taste.
Add the garlic, then cook for 30 seconds.
Remove the vegetables from the pan. Place them on the plate with the ham and cover to keep warm.
Pour the remaining teaspoon of oil into the pan. Add the eggs and cook, stirring occasionally and breaking up with a spatula, until the eggs are scrambled, about 3 minutes. Season the eggs with salt and pepper to taste.
Add the rice, ham, cooked veggies and peas into the pan. Stir to combine.
Stir in the soy sauce and sesame oil and cook until everything is thoroughly combined and warmed through, about 4-5 minutes.
Sprinkle green onions over the top of the fried rice, then serve and enjoy.