Preheat oven to 400°.
Add the chicken, zucchini, onions, and mushrooms to a large-rimmed sheet pan. Mix ¼ cup soy sauce, 1 tablespoon olive oil, and 1 tablespoon sesame oil and drizzle over the chicken and veggies. Season with ½ teaspoon black pepper, and 1 teaspoon garlic powder. Toss everything together and bake in a preheated oven for 10 minutes.
Add the cooked rice, frozen peas, carrots, and the remaining ½ cup soy sauce to a large mixing bowl. Stir together and set aside.
Remove the sheet pan from the oven and transfer the chicken and vegetables to a plate.
Spread the rice mixture on the sheet pan and top with chicken and vegetables. Place 4 tablespoons unsalted butter on top of the rice, chicken, and vegetables. Return to the oven, and bake for 5-10 minutes.
While the chicken and rice cook, scramble the eggs in a skillet on the stove.
Remove the sheet pan from the oven, add the scrambled eggs, and stir to combine.
Sprinkle with green onions and sesame seeds. Serve immediately.