Thanks to replies in the "Report a Problem" section, we found a workaround.
The problem seems to be OS X 10.11.1 related and how it interacts with Microsoft Outlook (2011).
Based on their suggestions, we opened Mail, set it as the default application but left Outlook set as the default application, as well. For some reason, this worked. Now, when we select a 'send mail' function, the email is composed and presented in Outlook to edit before sending (or sent automatically when the "Perform without dialogue" option is selected).
I know this isn't ideal, but it will work until the OS X bug is fixed.
This was a major issue for us as many of our routines trigger automated emails.
Have a great Sunday!