Preheat the oven to 350º Fahrenheit. Grease two 8” cake pans with shortening, then dust with flour. You can also line the bottom of the pans with parchement paper so they come out easily.
In the bowl of a stand mixer, combine the cake mix, eggs, butter and milk. Using the whisk attachment, beat on medium speed for 2-3 minutes until well combined. Scrape the sides of the bowl as needed.
Divide the batter evenly between the two pans.
Bake for 20-25 minutes until the top springs back when you touch it.
Allow the cakes to cool in the pan for 5 minutes, then turn them out onto a wire rack to cool completely.
MAKE THE FILLING:
Start making the filling while the cakes are baking because it will have to cool.
In a small saucepan over medium low heat, cook the flour and milk together, whisking constantly, until the mixture thickens to a pudding consistency. The amount of time this takes will depend on your pan and stovetop. Don’t turn the heat up too high or the milk may scorch.
Remove from the heat and allow the mixture to cool completely. (Move the mixture to another bowl and place it over a bowl of ice for it to cool more quickly.)
While the mixture is cooling, place the sugar in a food processor and pulse several times to make the granules a little finer.
Using a mixer, cream the butter, shortening, salt and vanilla until smooth. Scrape the sides of the bowl as needed.
Add in the processed sugar and beat for 2 minutes.
Add in the cooled flour mixture. Use a mixer and beat until the mixture becomes fluffy like whipped cream. This may take a couple of minutes.
ASSEMBLE THE CAKE:
Place one cake layer on a cake plate. Place parchment paper under the edges of the cake so that the plate doesn’t get messy when you are drizzling the glaze over the cake.
Spread the whipped filling over the cake.
Place the second cake layer on top.
MAKE THE WHITE CHOCOLATE GLAZE:
Melt the white chocolate and shortening together in the microwave in 30 second increments. Stir in between each interval.
Allow the mixture to sit for 3-5 minutes to cool slightly.
Slowly pour the glaze over the cake, working quickly to push it to the sides so that it runs over the edges and covers them. Be sure to work quickly because the chocolate may set quickly as it touches the cooler cake.
Remove the parchment paper from under the edges of the cake. If the chocolate has hardened, you may need to use a knife to cut around the bottom edge of the cake so the chocolate doesn’t pull off.
Melt the semi-sweet chocolate chips in a microwave safe bowl. Stir every 15 seconds until they are melted.
Place the chocolate in a small zippered bag and snip the corner of the bag.
Squeeze to make zebra cake lines over the top of the cake.
Store the cake in the refrigerator in an airtight container.