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, and it looks like it jumped genres quite often.
Beck's version is on a home tape,
Beck and Dava, which seems to be a recording of a little get-together in someone's house, in which Beck and friends sing songs and chat.
After completing Woody Guthrie's "Those Brown Eyes," Beck notes that he knows another song about brown eyes. He sings a short bit of this, trying to remember it, but does not get very far.