If I ask for eggs, sunny-side-up, they will have yellow barely cooked yolks. At home I avoid this by placing a lid and creating hot air or steam that cooks the top more thoroughly. How do I ask for this style at a restaurant? What term do I use?
There are two different techniques possible here – obviously, simply frying for a longer time will cook the yolk more thouroghly. You might order this as “sunny-side up, well done”.
However, what you achieve by cooking with a lid isn't really considered just frying, but Basting, so what you want to ask for is probably a basted egg.