Preheat the oven to 180 degrees C. Lightly grease a 20 cm round cake pan with melted butter and cut out a round of nonstick baking paper to line the base of the pan.
Using an electric mixer, beat the butter, caster sugar and vanilla extract in a medium bowl until pale and creamy. Add the beaten egg gradually, mixing well after each addition.
Sift the self-raising flour and plain flour together. Mixing with a wooden spoon, add the flours to the butter and sugar mixture in two batches, alternately with the milk.
Spoon the cake batter into the prepared pan and smooth the surface with a spatula. Bake for 30 minutes, or until cooked when tested with a skewer. Allow the cake to stand in the pan for 5 minutes before turning out on a wire rack.
Combine the caster sugar and ground cinnamon. While the cake is warm, brush the top with melted butter and sprinkle with the sugar and cinnamon mixture. Serve the cake warm or at room temperature.
Alternatively, this cake is delicious iced with lemon icing (see footnote).
To make the lemon icing, put 1 1/2 cups icing sugar in a bowl and add enough lemon juice to make it a barely pourable consistency (the strained juice of 1-2 lemons). Spread over the cooled cake and leave to set.