What do you call eggs prepared with a broken yolk, in a skillet, with no char?
Where I come from, that would be called 'over hard.' 

As a reference, the others would be over-easy (runny yolk), over-medium (soft, slightly runny), and the over-hard would be cooked solid. 

Chefs will often break the yolk on an over-hard order, before flipping the egg, if it's not already broken.