Preheat oven to 325F degrees.
In a 10- or 12-inch nonstick skillet (I used a 12-inch, but for a thicker frittata, use a smaller skillet), heat 2 tablespoons oil over medium heat. Add the carrots, mushrooms, green onions, and green peas. Sauté until the vegetables begin to soften, about 3 minutes. Add the cooked rice and stir until the rice and vegetables are evenly combined.
In a medium bowl, whisk together 4 eggs, 6 egg whites, ¼ cup milk, ¼ teaspoon pepper, 2 Tablespoons soy sauce and 2 teaspoons hot sauce. Pour egg mixture into skillet and make sure vegetable and rice are evenly distributed.
Transfer skillet to the oven and bake 15-18 minutes, or until set and top begins to golden.
Remove from oven, cut as desired and serve immediately with extra vegetables and sauce of your choice.