Preheat oven to 350*. For bread pudding, tear baked biscuits into bite-size pieces. In a large bowl, combine biscuits and milk; set aside, In a medium bowl, beat eggs, melted butter, and vanilla until well blended. Add sugar and cocoa; beat until well blended. Stir in chocolate chips. Add chocolate mixture to biscuits mixture; stir until well blended.
Pour into a greased 8-inch glass baking dish. Bake 55 to 60 minutes or until set in center and edges pull away from sides of pan.
For Caramel Sauce, combine butter, sugars, and milk in a medium sauce pan. Stirring constantly, cook over low heat until butter melts ans sugars dissolve. Increase heat to medium and bring to a boil. Stirring constantly, boil about 9 minutes or until thickened. Remove from heat; stir in vanilla. Cut warm bread pudding into squares and serve with warm sauce.