Place a sheet pan on the middle oven rack and heat to 450 degrees.
In a large bowl, combine the cooled rice with salt, 2 tablespoons of the soy sauce, sesame oil and half of the diced onion. Toss to combine well. Remove the sheet pan from the oven, and spread the rice out evenly. Bake for 15 minutes.
1 tsp salt, 2 tbsp soy sauce, 2 tbsp sesame oil, 1 onion
While that cooks, make the sauce. In a medium saucepan on medium-high heat, add 1 tbsp neutral oil and the remaining diced onion. Cook for 1 to 2 minutes until the onions start to soften, then reduce heat to medium and cook for 2 minutes more until translucent.
½ cup neutral oil, 1 onion
Add most of the remaining neutral oil except about 1 tbsp, along with the mushrooms, garlic, ginger, 2 tablespoon soy sauce, and red-pepper flakes. Reduce heat to medium-low and cook for 10 to 12 minutes, until the mushrooms are completely soft. If the oil bubbles too much, reduce the heat to low.
½ cup neutral oil, 6 oz great mushrooms, 4 cloves garlic, 1 inch ginger, 2 tbsp soy sauce, 1 tsp red-pepper flakes
After 15 minutes, remove the sheet pan from the oven, add the frozen mixed vegetables and toss with the rice to evenly distribute. Make 4 to 6 divots in the rice (depending on how many eggs you are using), drizzle a tiny bit of neutral oil into each divot to prevent sticking, and break an egg into each. Return to the oven for 6 to 10 minutes until the whites are set but the yolks are still runny.
16 oz frozen mixed vegetables, 6 eggs
To serve, spoon some of the sauce over the rice and top with scallions. If the rice needs more seasoning, add more sauce or season with salt.
2 scallions