Cat Cora The DUI Mug Shot (Well Done)

7/11/2012 1:42 PM PDT

Cat Cora -- The DUI Mug Shot

TMZ has obtained Cat Cora's mug shot ... taken 11 days after the celebrity chef was arrested for DUI in Santa Barbara.

The Food Network chef was popped for drunk driving on June 17 -- after she rear-ended another vehicle ... and proceeded to call the people in the other car "nerds."  Cops say her blood alcohol level was more than twice the legal limit.

Cat was released hours after she was arrested ... but never took her mug shot.

But on June 28, Cat returned to the station to take her make up photo ... and it's pretty damn good as far as mug shots go.

Cat has since apologized for the arrest -- saying, “I deeply regret my decision to drive that evening after my designated driver became unavailable. I learned a very important lesson from this experience and take full accountability for my actions.”

Like we said, the mug shot's not bad at all ... so we gotta ask ...