Broadstock was born in Melbourne. He studied history, politics and music at Monash University and, later, composition and theory with Don Freund at the University of Memphis in the United States and with Peter Sculthorpe at the University of Sydney. The University of Melbourne awarded him the Doctor of Music degree in 1987.
From 1982 to 2006 Broadstock was employed in the Faculty of Music, University of Melbourne, as Professor of Music and Head of Composition. During 2007 he was a Vice-Chancellor's Fellow at the university.
In 2008 Broadstock's music was performed at the Opening Ceremony of the 2008 Summer Olympic Games and in 2009 he was Composer in Residence with the Melbourne Symphony Orchestra, composing a multi-instrumental concerto, Made in Heaven, for trumpeter James Morrison, a chamber concertino, Hall of Mirrors, for trombonist Brett Kelly and a symphony for soloists, choir and orchestra, Tyranny of Distance which was premiered at the 2009 Melbourne International Festival of the Arts.
Broadstock has won prizes for composition, including First Prize in the 1981 Townsville Pacific Festival's National Composition Competition for his orchestral work Festive Overture; two Albert H. Maggs Awards; two APRA Music Awards for his orchestral works The Mountain and Toward The Shining Light; First Prize in the Hambacher Preis International Composers' Competition, West Germany for his 'Tuba Concerto'; and in 1994 he received the Paul Lowin Song Cycle Award, Australia's richest composition prize, for 'Bright Tracks' for mezzo soprano and string trio. His orchestral work 'Stars in a Dark Night' (Symphony No. 2) received four 'Sounds Australian' National Music Critics' Awards including 'Best Australian Orchestral Work in 1989' and was the Australian Broadcasting Corporation's entry to the prestigious Paris Rostrum of Composers in 1990. In 2001 he received the Australian Music Centre's Victorian Award for Best Composition – 'Dark Side Symphony #5', and in 2002 his 'Federation Flourish' was nominated for an APRA/AMC "orchestral Work of the Year".
Prize for his solo piano work 'Dying of the Light' and in 1998 he received the Michelle Morrow Memorial Award for Composition and an Explorations Opera Project grant. In 1998 he spent three months in Italy on fellowships awarded by the Civitella Ranieri Foundation and a Bellagio Award from the Rockefeller Foundation. In November 2005 he returned to Italy as a fellow at the Ligurian Study Center in Italy.
In 1999 he received the prestigious Don Banks Award from the Australia Council, for his contribution to Australian Music, which enabled him to compose for most of that year, including visits to the USA (Visiting Professor of Composition at Indiana University), England and Russia. Five of his six symphonies were recorded by the Krasnoyarsk Symphony Orchestra (Russia) conducted by Andrew Wheeler and released on the Etcetera label in 2000 and received excellent reviews in England and Australia.
In 2004 Broadstock's solo piano work 'Torre di Forza' was the test piece at the Sydney International Piano Competition, and in 2005 ABC Classics released a CD of orchestral works performed by the Tasmanian Symphony Orchestra conducted by Ola Rudner. His chamber opera based on Ray Bradbury's Fahrenheit 451 was performed in Bonn, Germany in April 2006. His music is available on over 45 commercial CDs worldwide.
Since 2008 he has been a freelance composer and lives in Melbourne, Australia.
In the 2014 Australia Day Honours he was appointed a Member of the Order of Australia.