Combine all of the thai peanut sauce ingredients in a small, microwave-safe bowl. Heat for 20 seconds or until the peanut butter can be fully incorporated when stirred. (Alternatively, the sauce may be heated on the stovetop.) Set aside.
Whisk the eggs in a small dish. Heat 1 1/2 teaspoons of olive oil in a large skillet (12 inch diameter) or wok over medium-high heat. (If you need to cook chicken to use in this dish, you may cook it at this point, remove to a plate, wipe out pan, and then add an extra 1 1/2 teaspoons of olive oil before proceeding.) Pour in the eggs, and scramble until cooked but still a little glossy. Remove to a plate and chop.
Increase the heat to high, and heat the remaining tablespoon of oil in the pan. Add the cooked and cooled rice, spreading it into an even layer and pressing it down with a spatula. Sear the rice for about 2 minutes or until lightly toasted. Flip, press the mixture into an even layer again, and sear for 1-2 minutes more.
Add the mixed vegetables and green onions. Top with the chopped chicken. Before stirring, pour the soy sauce mixture over the chicken. (This allows for more even distribution of the sauce before it hits the more absorbent rice.) Then stir to fully incorporate and cook for about 2 more minutes or until all the ingredients are heated through, stirring in the eggs and half of the chopped peanuts during the final minute. Remove from the heat and garnish with the remaining peanuts.
Notes
Either brown or white rice may be used. I prefer long grain rice and day-old rice works best. If cooking the rice the same day as preparing the fried rice, spread the cooked rice on a platter or baking pan and refrigerate for several hours. After several hours, cover until ready to make the fried rice. This will allow the rice to dry out and firm up a bit. Optionally, a pint container of leftover takeout rice is ideal for this recipe. When preparing at home, 1 cup of dry rice will yield 3 cups cooked.