Cook the rice according to package directions. Spread the cooked rice in a single layer on a baking sheet and allow it to cool. Place the rice in the freezer for about 2 hours or so. (This can be made in advance.)
Remove the rice from the freezer and let it sit while you gather the remaining ingredients. Place the rice in a microwave-safe dish, add 4 tablespoons of water, and microwave for about 2 minutes, or until heated through. Set aside.
In a small bowl, combine the gluten-free soy sauce and gluten-free oyster sauce. Set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium heat. Add the eggs and scramble until cooked. Remove the eggs from the wok and set aside.
Season the pork generously with salt and pepper. Add the remaining 1 tablespoon of vegetable oil to the wok and cook the pork until cooked through and lightly browned.
Build the fried rice. Add the sesame oil, followed by the white parts of the green onions and the minced garlic. Stir to combine.
Add the frozen peas and carrots and stir.
Add the warmed rice to the wok. Spread it into a flat layer and allow it to cook for a few minutes, pressing it down occasionally, until the rice is heated through.
Pour the sauce over the rice. Add the cooked eggs and the green parts of the green onions, reserving a little green onion for garnish.
Stir everything together until well combined and heated through.
Garnish with the remaining green onions and serve hot.