Heat 1 teaspoon of the oil in a large skillet or wok over medium heat. Add the eggs and scramble until just set. Move them to a plate.
Add the remaining oil to the skillet and turn the heat to medium-high. Add the ham and cook for 2 minutes, until lightly browned.
Add the frozen peas and carrots and the garlic. Cook for 2 minutes, stirring.
Add the rice, breaking up any clumps. Cook for 3–4 minutes, stirring now and then, until the rice is hot and starting to crisp in spots.
Stir in the soy sauce, sesame oil and scrambled eggs, breaking the eggs into small pieces.
Top with the green onions and serve.