I've also been scratching my head on this since diving into the Outlook Integration and with the help of this Answer discovered a setup option in Lightning under Administration>Email called "Outlook Integration and Sync" that has a slider to "Use Enhanced Email" with Outlook" that solved my issue.

With "Use Enhanced Email with Outlook" enabled in addition to being able to log emails while sending all logged emails going forward have a new email style template that more closely resembles an email.