Break up the cold rice with your fingers until no clumps remain. Dice the onion and carrot small, about ¼ inch, so they cook in the same time as the rice. Season the chicken or shrimp with the salt and pepper. Mix the soy sauce, sesame oil, and sugar in a small bowl. Fried rice moves fast, so everything should be within arm's reach.

Heat a 12-inch carbon steel or cast-iron skillet over medium-high heat for 2 minutes. Add 1 teaspoon oil and 1 tablespoon butter. Add the chicken in a single layer and leave it alone for 2 minutes until golden underneath. Stir and cook another 3 to 4 minutes, until the center reaches 165°F and the juices run clear. For shrimp, cook about 90 seconds per side until pink and opaque. Move the protein to a plate.

Add the remaining oil and 1 tablespoon butter to the same pan. Add the onion and carrot and cook 3 to 4 minutes, stirring often, until the onion looks translucent at the edges. Add the peas and garlic and cook 30 seconds, just until fragrant. Push everything to one side of the pan so you have a bare patch for the eggs.

Pour the eggs into the empty space and stir gently for about 45 seconds. Stop when they are just set but still glossy. Break them into small curds with your spatula, then fold them into the vegetables.

Add the rice and the last tablespoon of butter. Spread the rice across the pan and press it down for 30 seconds so the grains toast, then toss. Repeat for 3 to 4 minutes, until the rice is hot all the way through and you hear a light crackle. Pour the soy mixture around the edges of the pan, not directly onto the rice, so it sizzles and caramelizes slightly. Toss well.

Return the chicken or shrimp to the pan and toss for 1 minute. Taste and add a splash more soy sauce if needed. Fold in the scallions, then serve right away while the rice is still steaming.