Heat a large skillet or wok over medium heat. Add 1 tablespoon of butter and allow it to melt.
Pour in the beaten eggs and let them cook undisturbed for 30-40 seconds until they begin to set. Scramble the eggs until just cooked through, then transfer to a plate and set aside.
Add the remaining 2 tablespoons of butter to the pan. Once melted, add the diced carrot and chopped onion. Cook for 3-4 minutes until vegetables begin to soften.
Add the minced garlic and cook for 30 seconds until fragrant, being careful not to let it brown.
Increase the heat to medium-high. Add the cold rice and frozen peas to the pan, spreading in an even layer. Let it cook undisturbed for about 1 minute to develop some crispiness on the bottom.
Stir the rice and repeat the process a couple more times, allowing the rice to crisp up a bit between stirs (about 3-4 minutes total).
Return the cooked eggs to the pan. Add the sliced green onions, soy sauce, sesame oil, and oyster sauce.
Stir everything together thoroughly until well combined and heated through, about 1-2 minutes more.
Season with salt and pepper to taste, keeping in mind that the soy sauce already adds saltiness.
Serve immediately as a main dish or as a side with your favorite Chinese-inspired entrées.