Preheat the oven to 375˚F / 190˚C. Grease a 6-inch (15-20 cm) baking tin.
Put butter, sugar, and vanilla extract into a bowl, and beat it well, until the consistency is creamy and lump-free.
Beat in the eggs, one at a time.
Finally, fold in the self-rising flour and mix well.
Pour the batter into the baking tin, and place in the oven.
Bake for 20-25 minutes, until risen and golden brown on top. The cake should be pulling away from the sides of the pan, and the top should spring back when gently pushed in the middle. A toothpick inserted in the middle will come out with only one or two little crumbs.
Let the cake cool in its pan for 10 minutes, then turn it out onto a wire rack and let it cool completely.