Funny you should say that. I would have said hard-boiled or scrambled up until about a month ago, but I've recently found that fried over-easy can be an excellent choice on certain sandwiches. Like pulled pork with bbq sauce, jalapenos and cheddar is somehow better with a tad of somewhat-runny egg yolk. Weird, I know, but true.
TPBM is willing to give such a sandwich a try now, and will keep an open mind about it if he/she refused fried eggs before.