Kristy Lee Cook, the Oregon singer who sold a horse to finance a trip to Philadelphia to audition for “American Idol,” has signed with 19 Recordings/Arista Nashville.  Cook’s first single, “15 Minutes of Shame,” will be released to country radio on Aug. 11. Cook will be recording her debut album with producer Brett James in between tour dates this summer. Album is penciled in for the fall. Cook is the third member of season seven of “American Idol” to secure a recording contract within the BMG roster of labels.