Jean Georges Ginger Fried Rice

Name: Jean-Georges' Ginger Fried Rice
Ingredients: 1/2 cup peanut oil if you're Mark Bittman, chicken fat if you're Jean-Georges; 2 tablespoons minced garlic; 2 tablespoons minced ginger; Salt; 2 cups thinly sliced leeks, white and light green parts only, rinsed and dried; 4 cups cooked rice, preferably jasmine, at room temperature (see note below); 4 large eggs; 2 teaspoons sesame oil; 4 teaspoons soy sauce