A damaged Braided Hair Large Cent. In this example the E was carved into a U, changing the word CENT into a slang term for female genitals. There may be better carved examples, but still not a mint error.
Another example of a carved coin are the Hobo Nickels, where the Indian Head is carved into something else like an Soldier or Hobo. Hobo Nickels have become a collectible.
However, neither example should be confused as a mint error or as being authorized by the U.S. Mint.