Preheat the Blackstone over high heat. Season the chicken with salt and pepper. Add 1 tablespoon vegetable oil to the griddle, spread the chicken in a single layer, and cook 2 to 3 minutes per side until browned and cooked through. Remove to a plate.

Add the remaining 1 tablespoon oil, then sauté the garlic, ginger, and white scallion parts for 30 seconds until fragrant. Add the peas and carrots and cook 2 minutes, stirring occasionally, until just tender.

Push the vegetables to one side. Pour the beaten eggs onto the empty spot, let set 20 seconds, then scramble until soft, about 1 minute. Mix with the vegetables.

Add the rice and break up clumps. Drizzle with soy sauce and sesame oil, toss to combine. Spread into an even layer, let sit 1 minute to crisp, toss, and repeat once more, cooking about 4 minutes total. Add the butter at the end and toss until melted.

Spoon into bowls, top with reserved green scallions, and drizzle with a little extra sesame oil if desired. Serve immediately.