Cream together the butter and sugar, until light and fluffy.
Add vanilla extract and eggs, and mix thoroughly.
In a separate bowl, whisk together the dry ingredients.
Alternating and starting with the dry ingredients in two additions, add the buttermilk and dry ingredients, mixing to combine.
Mix in grated carrot.
Pour batter onto sheet pan and use offset spatula to smooth out.
Bake for about 25 minutes, or until toothpick comes out clean and cake is cooked through (Ovens vary).
Let cool completely.
For the Icing:
Make the icing by whipping the cream cheese until it is smooth (scraping down the bowl – this is important or you will have lumps). Add the lemon juice and extract and mix, and finally add the sugar and beat until smooth.
Serve
Use offset spatula again to smooth icing on top of cooled cake. Refrigerate until needed, or serve immediately.
Notes
Homemade buttermilk is fine for this cake. To make it: add 1 tablespoon of vinegar to a one-cup measure and fill it the rest of the way with milk. Let sit for 5 minutes and then use in the recipe.