This was written by Eric Clapton and George Harrison. Harrison, who is listed on the album as "L'Angelo Misterioso," also played rhythm guitar on this, since Cream had only one guitarist: Clapton.
The title has nothing to do with the song. Clapton saw Harrison's notes for this, and misread "Bridge" as "Badge." He thought this is what Harrison named the song, so they used it for the title.
The lyrics are not intended to make sense. Many of them were taken from drunken conversations Harrison had with Ringo Starr.
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