- Preheat the oven to 350°F (180°C). Lightly grease three 8-inch (20 cm) round cake pans. Line the bottom of each pan with parchment paper and dust the sides with flour, tapping out any excess.
- Sift the flour, sugar, baking powder, baking soda and salt together into a large mixing bowl or into the bowl of a stand mixer fitted with the paddle attachment. Add the butter and work in using electric beaters or the mixer on medium-low speed until no pieces of butter are visible, about 2 minutes. Whisk ¾ cup (176 mL) of the buttermilk and the oil together and add this to the flour, mixing at low speed until combined. Whisk the remaining ½ cup (125 mL) of the buttermilk with the egg whites and vanilla, add at once to the batter and mix again at low speed until combined. Increase the speed to medium-high and beat well for about 3 minutes, until the batter is fluffy and thick. Stir the sprinkles into the batter by hand.
- Divide the batter evenly between the pans and spread the batter to level it. Bake the cakes for about 40 minutes, until a tester inserted in the centre of a cake comes out clean. Cool the cakes in their pans on a rack for about 20 minutes before turning out onto the racks to cool completely. Ideally, chill the cakes for at least 2 hours before assembling.
- For the frosting whisk the milk and flour together in a medium saucepan over medium heat until it thickens and just begins to bubble, about 4 minutes. Whisk in the sugar and salt and continue whisking over medium heat until the mixture begins to bubble again, about 3 more minutes. Pour the paste (it will look like a very pale pudding) into a dish and let this cool, uncovered until room temperature, 68-70°F (20-21°C).
- Check that your butter is just below room temperature (65°F/18°C). Using electric beaters or in a stand mixer fitted with the paddle attachment, beat the butter at medium-high speed until fluffy. Add the cooled milk paste in three additions, mixing well after each addition. Add the vanilla. Add food colouring to your liking and use the frosting immediately.
- To assemble the cake, place one cake layer on a cake turntable or platter and top with a generous amount of frosting, spreading to level. Top this with the second cake layer and repeat spreading the frosting, topping with the final cake layer. Spread a generous amount of frosting on the top of the cake, coaxing it to hang over the edge. Spread frosting to cover the sides of the cake, and use an offset spatula to smooth out the frosting, joining it to the frosting overhanging from the top.
- To decorate, use sprinkles to coat the sides of the cake and use any leftover frosting in a piping bag fitted with a decorative tip, to pipe decor on the top of the cake.
- If for some reason the frosting is not smooth, increase the speed and continue whipping – often the warmth generated by the friction of the beaters warms it a touch to allow the elements to blend smoothly.
- By its nature, the outside of the cake layers brown as it bakes. If you are seeking cake slices that showcase the white texture of the cake against the coloured frosting and sprinkles, you can trim away the browned cake on the outside. Chill the cakes for at least 2 hours and then use a serrated knife to shave away the brown cake as thinly as possible, and use a coarse rasp grater to shave away the brown from the round outside edge without compromising the round shape of the cake.