Preheat the oven to 170˚C fan-forced. Grease a 23 cm springform cake tin with butter.
In a large bowl, sift together the flour, baking powder, bicarb soda, salt and cinnamon. Add the eggs, vegetable oil, carrot, pineapple and sugar and mix well to a thick batter.
Pour the cake batter into the prepared tin and bake for 50-60 minutes or until a skewer inserted into the centre of the cake comes out clean. Remove from the oven and allow to stand for 10 minutes before removing from the tin to cool fully.
Once completely cooled, make the icing. Place the butter, vanilla and cream cheese into the bowl of a stand mixer with the paddle attachment fitted. Beat on medium speed until smooth, then gradually add the icing sugar and beat until light and fluffy.
Spread the cream cheese icing over the cooled carrot and pineapple cake. Cut into wedges to serve.
