Preheat the oven to 350 F (180 C), butter two 9-inch (or 8 inch) round cake pans and line the bottoms with parchment paper, then dust with flour.
In a bowl, cream together the butter and sugar until light and fluffy.
Add the eggs and beat well.
Add the baking powder, salt and vanilla and continue to mix.
Alternate with the milk and flour mixture in 2-3 batches, starting with the milk and ending with the flour. The batter may look slightly clumpy but this is normal and nothing to worry about. To make the process easier, you could also add all of the milk first and then the flour- you will get the same results. Alternating the ingredients may be easier to incorporate all of the flour and milk.
Gently stir in the sprinkles, mixing just to combine. Over-mixing will lead to a tougher cake texture and may also result in the sprinkles bleeding through the batter.
Bake the cakes for 25-30 minutes or until a toothpick inserted comes out clean. Cool completely before frosting.
To make the frosting, beat the butter, confectioners' sugar and vanilla until smooth.
Alternate the sugar with the milk, beginning with the sugar and ending with the sugar. Beat the mixture until completely smooth.
To frost the cake, remove the parchment bottoms. Place one of the cakes top- side down onto a cake stand and spread atop about 1/2 cup of the frosting. Sandwich with the other cake (bottom side down).
With about 3/4 cup of icing, cover the cake entirely in a very thin layer of frosting to seal in the crumbs. This is known as a crumb coat. Refrigerate the cake for 30 minutes or until the coat is dry to touch.
Cover the cake in the remaining frosting and decorate with sprinkles.