Preheat the oven to 180 C. Grease and flour a 23x30cm baking pan.
In a large bowl, beat together eggs, oil, caster sugar and vanilla essence. Mix in flour, bicarbonate of soda, baking powder, salt and cinnamon.
Stir in carrots and fold in pecans. Pour into the prepared pan.
Bake in the preheated oven for 40 to 50 minutes or until a skewer inserted into the centre of the cake comes out clean. Let cool in pan for 10 minutes, then turn out onto a wire rack and cool completely.
To Make the Topping: In a medium bowl, combine butter, cream cheese, icing sugar and vanilla essence. Beat until the mixture is smooth and creamy. Stir in chopped pecans. Spread over the top of cake when it has cooled.