American
Heat the oven to 180C and grease and line two 20 cm round cake tins.
Whisk the flour, baking powder, baking soda, cinnamon and salt together in a bowl.
In a second bowl, whisk the eggs with the brown sugar, oil and 1 tsp of the vanilla until smooth, then stir in the carrots.
Fold the dry ingredients into the carrot mixture until just combined and divide the batter between the tins.
Bake for 25-30 minutes, until a skewer comes out clean, then cool completely on a rack.
For the frosting, beat the butter until smooth, beat in the cream cheese briefly, then add the powdered sugar and remaining vanilla and beat until thick.
Sandwich the cakes with half of the frosting, spread the rest on top and chill for 30 minutes before slicing.