Preheat the oven to 350°F (175°C).
Grease and flour an 8-inch round cake pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In a large bowl, 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 dry ingredients and the milk to the butter mixture, beginning and ending with the dry ingredients. Mix until just combined.
Pour the batter into the prepared cake pan and smooth the top.
Bake for 28 to 30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake 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 fine crumbs form.
Add the vanilla frosting to the cake crumbs and mix thoroughly until the mixture holds together when pressed.
Roll the mixture into 1-inch balls and place them on a baking sheet lined with parchment paper.
Refrigerate the cake balls for at least 1 hour to firm up.
Melt the white chocolate candy melts in a microwave-safe bowl in 30-second intervals, stirring between each, until smooth.
Dip each chilled cake ball into the melted white chocolate, using a fork to fully coat it, then place back onto the parchment paper.
If desired, decorate with sprinkles before the coating sets.
Allow the cake balls to set completely at room temperature or in the refrigerator before serving.