The connector (double-sided) that is on most shields, but without the actual shield board.  To allow leaving a larger gap between boards (for heatsinking, or space for proto-board wiring on the double-sided connector protoboards.
...
----- <- other boards
-
-      <- gap connector
-
----- <- proto board
-
----- <- processor board
...
Pretty much like the ribbon connector but without the actual ribbon in the way.

This could also be used to jam a lipo in the gap between boards and keep things nice and clean.

I've actually used our bottom+top connector proto board for this purpose- you can trim it down to the first set of 0.1" holes, leaving about 20x8.5mm of board.

With this I was able to stuff a 70mAh lipo between a TinyScreen+ and TinyScreen for a double sided screen about 12mm thick

I don't see why you couldn't solder the male and female connectors back to back...

Just trim a protoboard down.

You would need a microscope to solder those headers together.