Mince the garlic cloves and thinly slice the scallions, keeping the white parts separate from the green parts.
In a large wok or nonstick frying pan, heat 2 tablespoons of vegetable oil over medium-high heat until it shimmers.
Add the minced garlic, scallion whites, and the frozen peas and carrots to the pan. Stir-fry for about 2 minutes until the vegetables are thawed.
Introduce the cold cooked rice to the pan, breaking up any clumps with your fingers as you add it. Toss everything together to combine.
Stir in the soy sauce, kosher salt, and ground white pepper until well mixed.
Push the fried rice to one side of the pan. On the empty side, add the remaining teaspoon of vegetable oil and crack the eggs into it.
Scramble the eggs until they are fluffy and almost set, then turn off the heat and mix them into the fried rice, breaking up any large pieces.
Drizzle the toasted sesame oil over the rice and toss everything together. Taste and adjust seasoning with more salt and white pepper if needed.
Garnish with the reserved scallion greens before serving.
