Can anyone identify this 40-pin SMT socket on the Silicon Labs BRD4180A board?
The key to this lies in the documentation for the BRD4001 'Wireless Starter Kit' which your BRD4180A plugs into - available from SiLabs here.
There you'll find the BOM spreadsheet, which tells you that the daughterboard connectors, P200 &amp; P201, are Samtec Tiger Eye™ TFC-120-02-L-D-A-K-TR - these are the connectors you'll need to use on your own boards to be able to re-use the BRD4180A on them.

The mating connectors on your BRD4180A are probably SFC-120-something....

The WSTK documentation package link is posted in a SiLabs Knowledge-Base article here.