Puree banana in a food processor. Add the sugar and eggs and whiz together. Add the butter and whiz until creamy. Add milk and vanilla and whiz until combined.
Scrape out and fold gently through the flour mixture.
Pour the batter into a silicone loaf pan, or kugelhopf. Smooth out the top. Bake for 40 minutes.
Notes
If you'd like to ice cake, whiz together: 1 cup cream cheese, 100g butter, 400g icing sugar and 1 tspn vanilla. Smooth over the cake once it has cooled.