First things first, preheat your oven to a toasty 350 degrees F (175 degrees C). While it's warming up, grease and flour a 10-inch springform pan. Grease it up real good!
Now, in a big ol' bowl, mix together the cake mix and instant pudding. Then, make a little well in the center and pour in those eggs, oil, and water. Give it all a good mix until it's nice and blended. Once it's all mixed up, spread it out evenly into that prepared pan.
Pop that pan into the oven and let it bake for about 45 to 50 minutes, or until a toothpick poked in the center comes out clean. Once it's done, let it cool completely on a wire rack before you try to take it out of the pan.
While the cake's cooling, let's work on the filling. Slice off about an inch from the top of the cake and set it aside for later snacking. Then, scoop out the center of the bottom part, leaving about an inch around the edges. You can save the scooped-out cake for later or just munch on it now—it's up to you!
For the filling, whisk together the flour and milk in a saucepan. Cook it over medium heat, stirring like crazy until it gets nice and thick. Set it aside to cool down completely.
Once that milk and flour mixture has cooled off, beat together the shortening, butter, sugar, and vanilla until it's light and fluffy. Then, add in the milk mixture and keep beating for about 4 more minutes. Spoon all that creamy goodness into the center of the cake and pop that top layer back on.
Now for the chocolatey glaze! In a double boiler, melt together the chocolate chips, shortening, corn syrup, and water. Keep stirring until it's all nice and smooth. Then, pour that warm glaze all over the top of the cake and smooth it out over the sides. Stick it in the fridge until you're ready to serve it up.
Serve up this indulgent treat and watch everyone's eyes light up with joy!