BCC every incoming and outgoing e-mail in Microsoft Exchange

You're looking for the journal feature in exchange. This can track every message sent and received to mailboxes in your exchange server. You define which mailboxes to journal, you define a mailbox that you want to receive the journal message (the BCC emails delivered to, if you like) and that's it.

You need to ensure that if you have mailbox limits, you lift these for the journal recipient as this will obviously be dealing in a lot of messages relative to a 'normal' mailbox in your organisation.

This is explained in more detail here. While this link talks about Exchange 2013, Exchange has supported mailbox journaling for quite some time.