Melt the butter in a pan over medium heat, sprinkle in salt and pepper, and add in the vegetables, garlic, and ginger. Cook for 3 to 5 minutes until the vegetables are soft and tender. Add in 2 tablespoons teriyaki sauce and mix to coat.
Add in the cooked rice, remaining 2 tablespoons teriyaki sauce, brown sugar, and garlic powder. Mix together over medium-low heat for about 2 minutes. Make four wells and crack an egg into each. Stir together to scramble the egg in the stir fry.