Combine the short-grain white rice with 2 cups of water in an Instant Pot, rice cooker, or covered saucepan. Add the tablespoon of cooking oil if using.
Cook according to the directions for the appliance being used, or prepare on the stovetop until the rice is tender.
Line a baking sheet with parchment paper and distribute the cooked rice across the surface in an even layer.
Refrigerate the rice for at least 1 hour. For a faster option, place it in the freezer for approximately 20 minutes. Cooling the rice before frying helps keep the grains separate and reduces clumping.
Cut the pork tenderloin into small, approximately 1/2-inch pieces.
Finely mince the garlic. Peel the carrots and cut them into a small dice, then finely dice the yellow onion.
If frozen peas are being used, thaw them before cooking. Thinly slice the green onions, retaining primarily the white portions along with some of the green tops.
Have all prepared ingredients ready before beginning the stir-fry so they can be added quickly during cooking.
Place a very large skillet, wok, or griddle over medium heat and melt 1 tablespoon of the butter.
Pour in the lightly beaten eggs and cook while stirring gently. Remove them from the heat while they are still slightly soft and just underdone, since they will finish cooking when returned to the fried rice.
Transfer the eggs to a separate plate and reserve.
Raise the heat to medium-high and melt 1 tablespoon of butter in the same cooking vessel.
Add the diced pork tenderloin. Cook while avoiding excessive stirring so the pork has an opportunity to develop browned surfaces.
When the pork is nearly cooked through, add the minced garlic and continue cooking for another couple of minutes.
Transfer the cooked pork and garlic to a plate.
Melt another 1 tablespoon of butter in the pan. Add the diced carrots, yellow onion, and peas.
Sauté the vegetables, stirring only from time to time, until they become tender and develop a light golden color.
Transfer the vegetables to the plate containing the pork.
Melt the final 2 tablespoons of butter in the pan.
Add the thoroughly chilled rice and arrange it in a uniform layer. Leave it undisturbed for a couple of minutes so that some of the rice along the bottom can become lightly crisp.
Stir the rice and continue cooking until it is heated throughout.
Return the browned pork, garlic, cooked vegetables, and any accumulated juices from the plate to the pan. Stir thoroughly to distribute them through the rice.
Add the reserved scrambled eggs, sliced green onions, 3 tablespoons of soy sauce, 1 teaspoon of toasted sesame oil, and 1 teaspoon of sesame seeds.
Stir until all ingredients are evenly incorporated and completely heated through.
Taste and season with salt and pepper as necessary. Add additional soy sauce or toasted sesame oil according to preference.
Serve the pork tenderloin fried rice warm.