Heat 1 tbsp cooking oil in a large wok or skillet over high heat. Add diced chicken, season lightly, and stir-fry for 3-4 minutes until golden. Remove to a plate.
Add 1 tsp oil to the pan, pour in whisked eggs, and scramble quickly for 30-45 seconds until soft curds form. Push aside.
Melt butter in the center, add garlic and ginger for 15 seconds, then add cold jasmine rice. Break up clumps with your spatula and fry on high heat for 2 minutes.
Add thawed peas, carrots, and cooked chicken back to the pan. Drizzle soy sauces and toasted sesame oil around the wok edges.
Toss vigorously for 1 minute until evenly coated in rich amber color. Fold in green onions and serve hot with sesame seeds.