According to the Cardinals website, the Cardinals have had 13 players manage for the Cardinals who eventually made the Hall of Fame. Of that list, seven players made it from their playing career, with six of them serving the duel roles of player-manager back when that was common (the exception is Red Schoendienst). Two others made the Hall of Fame as a manager not because of their work with the Cardinals (Bill McKechnie and Joe Torre) and one other made it from their work as a general manager (Branch Rickey).
That leaves three managers, two of which every Cardinals fan can name in their sleep, Whitey Herzog and Tony La Russa.