Heat 1 tablespoon oil in a large skillet or wok over medium heat. Pour in beaten eggs and scramble for 20 seconds until just set but still soft. Transfer the eggs to a plate; they will finish cooking when tossed back in later.
2 eggs, 2 tbsp vegetable or sesame oil
Add another 1 tablespoon oil to the same pan and increase heat to high. Add shrimp in a single layer and cook for 1-2 minutes per side until opaque and slightly firm. Remove the shrimp to the plate with the eggs.
1 lb shrimp, 2 tbsp vegetable or sesame oil
Add remaining oil to the pan. Toss in the day-old rice, breaking up clumps with a spatula. Let the rice sit undisturbed for 1-2 minutes to crisp the bottom, then stir and repeat. Add scallion whites, garlic, diced carrots, and peas (if using), and stir-fry for 2 minutes until fragrant.
3 cups cooked rice, 4-5 scallions, 3 cloves garlic, 0.5 cup frozen peas, 0.5 cup diced carrots, 2 tbsp vegetable or sesame oil
Pour soy sauce around the edges of the pan, stir for 1 minute to coat the rice evenly. Taste and adjust by adding more soy sauce or white pepper if needed. Return the cooked eggs and shrimp to the pan and toss for 30 seconds to warm through.
3 tbsp soy sauce, 0.5 tsp white pepper, 1 lb shrimp, 2 eggs
Toss in the scallion greens, stir for 30 seconds, then immediately transfer the fried rice to plates. Serve hot while the scallions still have a fresh snap.
4-5 scallions