So, one of your todos is to make your own broom. For that you need the special wood and then a head. It's important to say that after one head is attached, it's not possible to swap it, so make a save before combing the wood with any of the possible heads, then combine one of the heads and apply for a job on LeChuck's ship with Iron Rose (the quartermaster at the docks). Note that you also need to have a disguise to do so. Reload the game, use a different head and apply again.
The heads are:
- String found on the jetty outside the Scumm Bar kitchen
- Sponge found at the Stan's place of work (selling ships, now boarded up). It's by a rusty bucket
- Puppy dolls found at Carla's mansion
- Shrunken head found at the International House of Mojo, on a shelf