Broadhurst, a center, was selected by the Chicago Blackhawks in the seventh round (No. 199) of the 2011 NHL Draft. He spent two seasons with Green Bay of the United States Hockey League and one with London of the Ontario Hockey League before signing a three-year, entry-level contract on June 14, 2013. He made his professional debut with Rockford, the American Hockey League affiliate of the Blackhawks, the following season.
Before appearing in an NHL game, Broadhurst was traded to the Columbus Blue Jackets along with forward Brandon Saad for forwards Artem Anisimov, Corey Tropp, Marko Dano, Jeremy Morin and a fourth-round draft pick on June 30, 2015.