It’s Outlook, so it must be able to do this, right?

Right.

It’s really quite simple. Do this:

• Create a new message
• Click in the body of the message to get the blinking cursor in the right place
• Go to the Insert menu and select Object…
• Click the Create From File tab
• Browse to select the PDF file on your computer
• Click Okay

Voila. The PDF file should now appear in the body of your Outlook email.