Preheat the oven to 350°F (175°C). Grease and flour a 9x13 inch pan.
In a large bowl, beat together eggs, oil, sugar, and vanilla. Mix in flour, baking powder, baking soda, salt, and cinnamon. Stir in carrots and fold in walnuts. Pour into prepared pan.
Bake in the preheated oven for 40 to 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.