Cook rice according to package instructions. When finished, transfer to a large, shallow bowl and allow to cool in the refrigerator. Cold or leftover rice works best for this recipe.
Put frozen vegetables in a microwave safe dish with ~2 tablespoons of water. Cover and microwave for ~10-12 minutes.
In a large pan, warm 2 teaspoons sesame oil over medium heat. Add diced onion and sauté until golden brown. Push onions to the side, and warm the other 2 more teaspoons of oil. Add the diced chicken and cook until both sides are opaque and it is no longer pink inside, ~10 minutes.
Add the mixed vegetables, ground pepper and 1 tablespoon of soy sauce to pan with the chicken and onions. Stir well to combine ingredients, then push the everything to the sides, creating a hole in the middle of the pan. Crack both eggs in the center, allow to sit for a few seconds, then use a spoon to scramble the eggs. They should be in small pieces. Stir everything together, remove from heat and set aside.
In a separate large sauté pan, melt the 3 tablespoons of butter. Make sure the butter covers the evenly bottom of the entire pan. Add the rice in an even layer and allow to cook in the butter. Once the bottom layer begins to get crispy, use a spatula to flip so both sides get browned. Once browned, add 3 tablespoons of soy sauce and stir well. Add rice to the pan with chicken and vegetables and toss everything together. Serve immediately or store in an air-tight container for a quick meal during the week.