Combine sugar, oil, vanilla, and eggs. In a separate bowl, whisk together flour, baking soda, baking powder, salt, ginger, cloves, nutmeg, and cinnamon. Gradually mix dry ingredients into wet ingredients until smooth.
Fold in grated carrots and chopped pecans until evenly distributed.
Preheat oven to 350°F. Grease and flour two 9-inch round cake pans. Divide batter equally between pans and bake for 38-42 minutes, until a toothpick inserted comes out clean. Cool in pans for 10 minutes, then remove and cool completely on wire racks.
Prepare frosting: Beat softened cream cheese and butter until creamy, about 3 minutes. Add vanilla extract. Gradually add powdered sugar and milk, mixing on low speed until smooth. Spread frosting over cooled cakes.
Notes
This carrot cake is perfect for celebrations and pairs wonderfully with a cup of coffee or tea.