That's Good Luck Charm, by The King himself.
Here's another from 1962. The first line was spoken; the second was sung:
The words you used to whisper low
No other love can ever bring again
Love Grows (Where My Rosemary Goes) was performed by the British pop group Edison Lighthouse. The group didn't exist when the original recording was made by lead singer Tony Burrows and several studio musicians. When the song became a hit, Burrows realized that Edison Lighthouse would need a public face, so auditions were hurriedly arranged, and a band named The Greenfields was selected to perform with Burrows as Edison Lighthouse. They made their first public appearance as Edison Lighthouse a week after their audition.
Other bands occasionally filled in for The Greenfields, but, with Burrows as the front man, they were always billed as Edison Lighthouse.