Heat 1 tablespoon of oil in a large skillet over medium heat. Add beaten eggs and scramble until set. Remove and set aside.
In the same pan, heat 1 tablespoon of vegetable oil over medium-high heat. Add diced ham, frozen peas and carrots, minced garlic, and the white parts of the green onions.
Add the cold, cooked rice to the pan. Break up any clumps with a spatula. Stir-fry for 5 minutes until the rice is heated through and begins to brown.
Return the eggs to the pan. Stir in soy sauce and sesame oil. Mix well. Cook for 2 more minutes.