Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, using an electric mixer, beat the softened butter and granulated sugar together until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.
Alternately add the flour mixture and whole milk to the butter mixture, beginning and ending with the flour mixture. Mix until just combined.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 25 minutes or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool completely in the pan on a wire rack.
Once cooled, crumble the cake into a large bowl using your hands or a fork until it resembles fine crumbs.
Melt 4 ounces of the white chocolate with 1/2 tablespoon of vegetable shortening in a microwave-safe bowl in 20-second intervals, stirring between each, until smooth.
Add the melted chocolate to the cake crumbs and mix thoroughly until the mixture holds together and can be rolled into balls.
Using your hands, roll the mixture into 1-inch balls and place them on a parchment-lined baking sheet. Refrigerate for 30 minutes to firm up.
Melt the remaining 4 ounces of white chocolate with the remaining 1/2 tablespoon of vegetable shortening in the microwave using the same method.
Dip each chilled cake ball into the melted white chocolate, using a fork to coat completely, and place back on the parchment paper.
Allow the chocolate coating to set at room temperature or refrigerate for 15 minutes until firm.
Serve immediately or store in an airtight container in the refrigerator.