For Cake: Line 3 (9 inch) round cakepans with wax or parchment paper. Lightly grease and flour paper and set pans aside. Stir together first 4 cake batter ingredients. Beat eggs and next 4 ingredients at medium speed with an electric mixer until smooth. Add flour mixture, beating at low speed until blended. Fold in carrot and next 3 ingredients. Pour batter in prepared cake pans. Bake in a preheated 350F oven for 25 to 30 minutes or until toothpick comes out clean. If using a 9x13 inch pan bake for 40 minutes testing after 30 minutes. Drizzle Buttermilk Glaze evenly over layers; cool in pans on wire racks 15 minutes. Remove from pans and cool completely on wire racks. Spread Cream Cheese Frosting between layers and on top and sides of cake.
Buttermilk Glaze: Bring first 5 ingredients to a boil in a dutch oven over medium high heat. Boil, stirring often, 4 minutes. Remove from heat and stir in vanilla. Yield: 1 1/2 cups
Cream Cheese Frosting: Beat butter and cream cheese at medium speed with an electric mixer until creamy. Add powdered sugar and vanilla and beat until smooth. Yield: 4 cups.