Technically speaking, there’s only two: James Cook University (JCU) and the University of New South Wales (UNSW). For these universities, candidates not only need to apply via QTAC and UAC respectively, but also need to complete and submit a separate ‘written application’ provided by the university, which requires them to write out full responses to a series of specific questions.
For JCU, you’re also allowed to submit up to three reference letters along with this written application, so make sure to sort this out as early as possible—people are often busy with their own lives, and it takes time to write a good reference, so don’t leave it to the last minute to ask them!
In past years, Western Sydney University (WSU) has also sent out a separate written application that applicants need to complete as part of their admissions process, although it’s unclear whether or not they’ll do the same this year since they’ve now teamed up with Charles Sturt University to offer a Joint Medical Program. For reference, in the past WSU’s application was slightly different to JCU and UNSW: the WSU application was only sent out after interview offers were made, and applicants only had around 24–48 hours to complete and submit it.