Written by (or possibly 'collected by') AP Carter and first recorded by The Carter Family in 1928. The Carter Family were one of the first famous country bands, having been one of the acts recorded at the Bristol Sessions in 1927 in Bristol, Tennessee/Virginia (the town straddles the border, with State Street marking the divide between the two states, as anyone who knows the Steve Earle song Carrie Brown will know). The Bristol Sessions produced the first nationally distributed country music recordings and have been described as country music's 'big bang'. Bristol TN/VA manhole covers have Birthplace of Country Music on them; we're still waiting for the Birthplace of Trip Hop ones to be fitted in our Bristol.
So they were already national stars in the States when they recorded Will You Miss Me in 1928; they recorded another version in 1935. Our version is based on this version, featuring Woody Guthrie, Leadbelly, Cisco Houston, Sonny Terry, and Bess Hawes, obviously having a fine time:
Other notable versions include Emmylou Harris, June Carter Cash (who was the daughter of Maybelle Carter, one of the original band, and, of course, married to Johnny Cash), and Swedish country pop superstars First Aid Kit.