"Honey Don't" was written and recorded by Carl Perkins in 1956. Released as the B-side of "Blue Suede Shoes" (also written by Perkins, perhaps at the suggestion of Johhny Cash when they were headliners on Louisiana Hayride; accounts vary). It became one of the most successful two-sided hits in popular music history (when there were 45s with two sides), perhaps second only to Elvis Presley's "Don't Be Cruel" and "Hound Dog." Both songs have been covered many times, 'Honey Don't" most famously by the Beatles with Ringo's vocal, and "Blue Suede Shoes," of course, was made even more famous by Elvis.
Audio only
UPDATE: John Lennon on vocal (h/t Alex Lubet):