Preheat the oven to 180 degrees C. Grease and flour a 23x33cm baking tin.
Cake: In a large bowl beat together the eggs, oil, caster sugar and vanilla. Mix in flour, bicarb soda, baking powder, salt and cinnamon. Stir in carrots and fold in pecans. Pour into the prepared tin.
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.
Icing: In a medium bowl combine butter, cream cheese, icing sugar and 1 teaspoon vanilla. Beat until the mixture is smooth and creamy. Stir in chopped pecans. Spread over the top of cake when it has cooled.