Bake the Cake: Prepare the yellow cake mix according to the package instructions. Pour the batter into a greased 9x13-inch baking dish and bake as directed. Let it cool for 10 minutes.
Poke the Cake: Using the end of a wooden spoon, poke holes all over the cake, making sure to go deep enough to allow the filling to seep in.
Prepare the Filling: In a medium bowl, whisk together the vanilla pudding mix and cold milk until smooth and thickened. Pour the pudding over the cake, spreading it evenly so it fills the holes. Refrigerate for at least 1 hour to allow the pudding to set.
Make the Chocolate Ganache: In a small saucepan, heat the heavy cream over medium heat until it just begins to simmer. Remove from heat and pour over the chocolate chips and butter in a heatproof bowl. Let sit for 2 minutes, then whisk until smooth. Stir in the vanilla extract.
Top the Cake: Pour the ganache over the chilled cake, spreading it evenly to cover the surface. Refrigerate for another hour, or until the ganache is set.
Serve & Enjoy: Slice and serve chilled. Enjoy this creamy, chocolatey, and utterly irresistible Boston Cream Poke Cake!