Anyone know what this is called?

[Toadrice]

The one of the screws

keeping the double sided handles on my barn doors snapped in half and I wanted to replace it but i'm having a hard time finding a replacement. Anyone happen to know what these suckers are called?

 

[AC Power]

I know this sounds odd, but they "socket connecting" furniture bolts. There a got to 10,000 different furniture fasteners. The are particularly used in places where the fastener (in your case it's the bolt) needs be countersunk, appear esthetically acceptable and have no convex texture to its feel. If you have countersinking drill bit and car to get to hardware place.....bring handles with you.

Best Luck.