Mince 3 garlic cloves. Thinly slice 2 medium scallions crosswise on a slight diagonal, keeping the white parts separate from the light and dark green parts.

Heat 2 tablespoons of the vegetable oil in a large wok or nonstick frying pan over medium-high heat until shimmering. Add the garlic, scallion whites, and 1 cup frozen peas and carrots. Stir-fry until the carrots and peas are thawed, about 2 minutes.

Add 4 cups cold cooked rice, breaking up any clumps of rice with your fingers as you add it in. Toss to combine with the peas and carrots. Add 1 tablespoon soy sauce, 1 1/2 teaspoons kosher salt, and 3/4 teaspoon ground white pepper. Stir to combine.

Push the fried rice to one side of the pan. Add the remaining 1 teaspoon vegetable oil to the now-empty side of the pan, then crack 2 large eggs into the oil. Scramble into fluffy curds until almost set.

Turn off the heat and stir the eggs into the fried rice, breaking up any large pieces of egg. Drizzle with 3/4 teaspoon toasted sesame oil and toss to combine. Taste and season with more kosher salt and white pepper as needed. Garnish with the reserved scallion greens.