Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, mix together flour, sugar, baking powder, baking soda, cinnamon, and salt.
Stir in the grated carrots.
In another bowl, beat the eggs, then add the oil and vanilla extract.
Combine the wet ingredients with the dry ingredients and mix until well blended.
Pour the batter into the prepared pan and bake for 40 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool completely before frosting.
For the frosting, beat together the cream cheese and butter until smooth. Gradually add the powdered sugar and vanilla extract, and mix until creamy.
Spread the frosting evenly over the cooled cake.