In a 3- to 4-quart saucepan or skillet, heat 1 tablespoon of sesame oil over medium heat. Add the scallion whites, 1/4 teaspoon of salt, and a pinch of pepper. Cook, stirring often, until tender but not browned, about 5 minutes.
Add the rice and cook, stirring often, until it begins to crackle, 2 to 3 minutes.
Add the chicken broth, lime zest, 1 teaspoons salt and 1/4 teaspoons pepper; bring to a boil. Cover and turn the heat down to low. Cook until the rice is tender and the liquid is absorbed, about 18 minutes. The trick to perfect is rice is not to lift the lid or stir during this stage. Leave it alone until all the liquid is absorbed.
Remove from the heat and using a fork, fluff the scallion greens, 1 tablespoon of sesame oil, and the lime juice into the rice. Let rest 5 minutes.