Heat 2 tablespoons oil in a wok or large skillet over high heat until it just begins to smoke.
Add the minced garlic, minced ginger, chopped onion, and chopped carrots; stir-fry for about 3 minutes until vegetables soften.
Add the chicken pieces, season with kosher salt and black pepper, and stir-fry until the chicken is cooked through and no longer pink, about 4 minutes.
Push the vegetables and chicken to one side of the wok. Pour the beaten eggs into the empty side and let them set briefly, then scramble and immediately add the day-old rice.
Toss the rice with the eggs so the grains are coated and take on a golden color, using a spoon or spatula to break up any clumps.
Stir in the soy sauce, oyster sauce, and sugar, mixing until the rice is evenly coated and turns a golden brown.
Combine the pushed vegetables and chicken back into the rice and mix thoroughly.
Stir in the frozen peas and most of the chopped scallions, reserving some scallion for garnish; toss to combine and heat through.
Transfer the fried rice to a platter or plates, garnish with the remaining scallions, and serve immediately with extra soy sauce if desired.