Heat 1 tbsp oil in a large skillet or wok over medium-high. Season chicken with salt and pepper and cook until no longer pink, 5–6 minutes; remove and set aside.
Add remaining oil; sauté onion until soft, about 2 minutes. Add garlic (and ginger if using) and cook 30 seconds.
Push veg to the side, pour in eggs and scramble quickly. Mix eggs with veggies.
Add rice, peas and carrots, and cooked chicken back to the pan. Stir to combine and break up rice clumps.
Pour soy sauce and sesame oil over mixture; toss until evenly coated and heated through, about 3 minutes. Stir in green onions and adjust seasoning.