Preheat the oven to 180°C (350°F) and line 2x 15cm (6 inches) round cake tins with oil and parchment paper.
Add the oil, butter, and sugar to a bowl of a stand mixer fitted with a paddle attachment. Beat at medium-high speed until light and fluffy, about 4 minutes.
Add the eggs to the butter and sugar mixture one at a time. Beat well between each addition and scrape down the sides of the bowl often.
Sift together the salt and self-raising flour then add the flour mixture to the egg and sugar mixture. Beat at low speed until just combined.
Combine the milk and vanilla extract in a jug, and slowly pour this into the cake mixture with the mixer's motor running at low speed. Scrape down the sides of the bowl and mix again, making sure it is lump-free.
Pour the cake batter into the prepared cake pan and bake in a preheated oven for 40 minutes or until a cake tester inserted into the center of the cake comes out clean. Allow the cake to cool in its tin for 30 minutes, before turning it onto a wire rack to cool completely.
Vanilla Frosting
To a bowl of an electric mixer fitted with a whisk attachment, add the butter. Beat at medium-high speed until the butter is light in color and well whipped.
Sift the icing sugar over the whipped butter and beat again, at medium-low speed to begin with, and then increase the speed to medium-high. Beat until fluffy, about 4 minutes.
Add the milk and vanilla to the frosting mixture, and beat until light and fluffy, scraping down the sides of the bowl often.
Transfer the frosting to a piping bag and use immediately.
Decorating
Level the cake layers with a serrated knife if necessary.
Secure the first cake layer onto a cake plate with a bit of frosting. Pipe a layer of frosting over the surface of the cake and smooth this out with a spatula.
Place the second layer of cake onto the first layer with the cut side facing down.
Pipe the frosting over the tops and sides of the cake and use a spatula or cake scraper to even this out. Decorate with sprinkles and candles. Enjoy!