Break up any clumps in the cold rice before you start cooking.
Heat 1 tablespoon oil in a large skillet or wok over medium-high heat. Add the eggs and scramble just until set, then transfer to a plate.
Add the remaining oil. Cook the garlic and the white parts of the green onions for about 30 seconds.
Add the peas and carrots, then the cooked chicken. Stir-fry until the chicken is hot throughout.
Add the cold rice. Press and toss it around the pan for 3 to 4 minutes so it heats evenly and gets a little toasted.
Return the egg to the pan. Add soy sauce, sesame oil if using, black pepper, and the green onion tops. Toss well and serve hot.