Brady's specialization is in rabbinic literature and the targumim, especially Targum Lamentations. He is the author of The Rabbinic Targum of Lamentations: Vindicating God, as well as several articles, book chapters and presentations in the field.
Raised in Montgomery Village, Maryland, Brady went to high school in Damascus, Maryland, received a B.A. from Cornell University in History and Near Eastern Studies, an M.A. from Wheaton College, Illinois in Biblical and Theological Studies, and a graduate diploma in Jewish Studies from the Oxford Centre for Hebrew and Jewish Studies at the University of Oxford and a D.Phil. in Oriental Studies from the University of Oxford. He was a member of St Cross College. His first post-doctoral appointment was to Tulane University.