Tommy has said that he did it on Electric playground.

He is credited as working on the soundtrack many places but he has a large list of games he has worked on and EarthWorm Jim is on the list. It has a page for it but it's blank, so I don't really know how much he worked on it.

Check out the blank page here

 Also the Wiki has Mark miller as the official composer and Tommy as the uncredited composer, so it seems likely that they both worked on it.

From the Wiki:
Mark Miller (credited composer)
Tommy Tallarico (uncredited composer)

Thanks Ben, we had checked the Wiki but it's a wiki so we weren't sure.

my guess is that they both worked on different tracks. or maybe one worked on the Bald Mountain remix.....