Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch pan/2 loaf tins.
In a large bowl, beat together eggs, oil, white sugar and 2 teaspoons vanilla. Mix in flour, baking soda, baking powder, salt and cinnamon. Stir in carrots and fold in nuts. Pour into prepared pan/tin.
Bake in the preheated oven for 40-50 minutes, or until a toothpick inserted into the center of the cake comes out clean. Let cool in pan for 10 minutes, then turn out onto a wire rack and cool completely.