This is the best carrot cake recipe I have ever tasted, and it is my mom's recipe that my family has enjoyed for many years.
Preheat oven to 350 degrees.
In a large mixing bowl, mix together all dry ingredients - flour, baking soda, salt, cinnamon and sugar; set aside.
In the bowl of your stand mixer (or other large bowl if you are using a hand mixer), beat together the eggs, oil, and vanilla.
With the mixer on low, slowly incorporate dry ingredients and shredded carrots, mixing until just combined.
Pour into 2 greased 9-inch cake pans. Bake until toothpick comes out clean, about 35 minutes.
Combine the cream cheese, butter, powdered sugar and vanilla, and beat with a mixer until smooth. Start out at a low speed, and gently ramp up until it looks like frosting (about a minute).
Add walnuts in last, and beat a few seconds to incorporate.
Frost the cake only after it has cooled completely.
If you are allergic to walnuts, pecans make a great substitute.