Heat 2 tablespoons oil in a wok or large skillet over high heat until just beginning to smoke.
Add the minced garlic, minced ginger, chopped onion, and chopped carrots; stir-fry for about 3 minutes until vegetables are softened.
Add the chicken pieces, season with kosher salt and black pepper, and stir-fry until the chicken is no longer pink, about 4 minutes.
Push the vegetables and cooked chicken to one side of the wok. Pour the beaten eggs into the empty side and scramble briefly, then immediately add the day-old rice.
Use a spatula to work the rice into the eggs until the rice is evenly coated and turns golden yellow.
Stir in the soy sauce, oyster sauce, and sugar, mixing until the rice is uniformly coated and has a golden-brown color.
Mix the vegetables and chicken back into the rice and stir until fully combined.
Add the frozen peas and most of the chopped scallions (reserve some for garnish), stir to heat through, and adjust seasoning if needed.
Transfer to a serving platter or plates, garnish with remaining scallions, and serve immediately with extra soy sauce if desired.
