You own thecheesecakefactory.com and your site lives there. You know that many of your visitors will simply type cheesecakefactory.com into their browser, so you purchase that domain as well.
What is the cleanest way of handling the redirection. I know GoDaddy offers a "domain forwarding" service but I am not sure if this is the "proper" way of handling it, and I don't necessarily like the idea of GoDaddy handling my DNS.
My other option would be sending the domain to my DNS servers and possibly my actual server. Is it possible to do this without setting up a new vhost and a 301 redirect on my server (using DNS only)? If not, how does the GoDaddy forwarding service work?
Update: Solution Below
This is not possible with a CNAME record only (see the chosen answer), it needs to be done on the server level. I ended up implementing a catch-all vhost on my server and pointing the new domain to my server with a simple A record. Here is what I used for a vhost:
<VirtualHost *:80>
# Catch all
DocumentRoot /var/www
ServerName cheesecakefactory.com
ServerAlias cheesecakefactory.com www.cheesecakefactory.com
# Re-direct
RewriteEngine On
RewriteRule .* http://thecheesecakefactory.com%{REQUEST_URI} [R=301]
</VirtualHost>