Never heard of this duet until I saw it on Miss Cellania recently. I went on a search to find out more about this arrangement and found many YouTube videos. This first one is the one that got me started.
Wikipedia had this to say about the duet: "While the piece is typically attributed to Gioachino Rossini, it was not actually written by him, but is instead a compilation written in 1825 that draws from parts of his 1816 opera, Otello. The compiler was likely the English composer Robert Lucas de Pearsall, who for this purpose used the pseudonym "G. Berthold"
Two young ladies performing the same piece.
Another from the BBC:
Looked for the banjo version of this but couldn't find one. May just have to work up an arrangement.