The Song:"Beautiful Brown Eyes" is an old country song. It has been covered by many many artists. I am not clear who did it originally.
Beck's version is on a home tape,
Beck and Dava, which seems to be a tape of a little get-together in someone's house, in which Beck and Dava sing songs and chat. They start talking about this old song, Beck sings a verse of it, with an exaggerated country falsetto vocal.