Sift the flour, baking soda, cinnamon and salt into a bowl. In a separate large bowl beat the eggs and oil together. Add the sugar and beat until light and fluffy. Add the vanilla and beat just until incorporated.
Fold the grated carrots into the egg mixture Fold in the flour and beat batter for 1 minute. Pour into a prepared baking pan. Bake for 25-35 minute or until a toothpick inserted in the center comes out clean.
Cool completely. While the cake is cooling beat the cream cheese and butter together until smooth. Beat in vanilla extract. Add powdered sugar one cup at a time. Beat until smooth and creamy.