Contact Form On Dashboard – How To?

I’m creating a theme and I’d like to implement a contact form widget to the admin dashboard so users of my theme can report any theme bugs to me. So it will be a widget with just one textarea and a send/report button.

I’ve been looking all around Google, but I’m finding plugins. I’m not looking to install a plugin. I need to write a simple form and slap it onto the admin dashboard. Is there a site or anything in the codex that can explain how to do that?