In a large skillet, heat 1/4 cup oil over medium heat. Add garlic and ginger and cook, stirring occasionally, until crisp and brown. With a slotted spoon, transfer to paper towels and salt lightly. Alternately, you can pour the oil into a heat-proof bowl through a fine-mesh strainer, then return the flavorful oil to the pan, reserving the ginger and garlic bits.
Reduce heat under skillet to medium-low and add 2 tablespoons oil and leeks. Cook about 10 minutes, stirring occasionally, until very tender but not browned. Season lightly with salt.
Raise heat to medium and add rice. Cook, stirring well, until heated through. Season to taste with salt.
In a nonstick skillet, fry eggs in remaining oil, sunny-side-up, until edges are set but yolk is still runny.
Divide rice among four dishes. Top each with an egg and drizzle with 1/2 teaspoon sesame oil and 1 teaspoon soy sauce. Sprinkle crisped garlic and ginger over everything and serve.
Note: Use leftover cooked rice if you have it. Here are some tips if you're cooking the rice fresh, to make sure it isn't too soggy: When the cook time is done, leave the rice undisturbed in the pot (uncovered) for 5 minutes. Spread the rice on a tray (or two) to dry out. While you prep the rest of the ingredients, put it by an open window or a fan, or pop the tray in the fridge or freezer if you have room. Jaden Hair at Steamy Kitchen also recommends starting with 1/4 to 1/3 less water when cooking the rice.