I like butter best, but my granny always used bacon grease, which was very good.
Here is how I cook mine, which are called Black Eggs:
Bacon fat, about a quarter inch worth, nice and hot, but not smoking.
Drop the eggs in, salt.
Enough black pepper to make the eggs more black than white.
Add crushed red pepper to eggs while the whites are still runny. If you wait until the whites cook, you waited too long.
Cook until the edges are crispy and brown, and baste the runny whites around the yolk liberally with hot bacon grease.
Remove eggs, Place buttered sourdough or scali bread butter side down into the hot bacon grease, and fry until crispy on one side.