Prepare and bake the cake in a 13x9 pan according to the package instructions. Let cool completely before poking holes across the cake with the bottom of a wooden spoon. Be sure to poke all the way to the bottom of the pan.
In a large bowl, whisk together pudding, milk, and vanilla, but don't let it thicken, Pour the thin pudding over cake in an even layer, poking down into the holes if necessary.
Refrigerate the cake for one hour.
Place the chocolate chips and corn syrup in a heat-proof bowl.
In a small saucepan over low heat, warm the cream until it simmers, stirring occasionally. Alternatively, you can microwave the cream until hot.
Pour hot cream over chocolate chips and let sit for 2 minutes to melt.
Stir until smooth. Let the glaze cool for 10 minutes.
Pour glaze over cake and smooth with a spatula. Chill cake for 4 hours or overnight before serving.