Preheat oven to 350 degrees F. Grease and flour 8" square or round cake pan (or line with parchment paper). Set aside.
In a large mixing bowl, whisk together flour, sugars, baking powder, soda, cinnamon, ginger and cloves.
1 cup all-purpose flour, ½ cup granulated sugar, ¼ cup packed brown sugar, 1 teaspoon baking powder, ¼ teaspoon baking soda, ½ teaspoon ground cinnamon, ¼ teaspoon ground ginger, ⅛ teaspoon ground cloves
In a large measuring cup, whisk oil with eggs. Add vanilla and whisk well.
2 large eggs, ½ cup canola oil, ½ teaspoon vanilla extract
Add wet ingredients to dry ingredients and stir in with a wooden spoon.
Add carrots and stir in well.
1 ½ cup shredded carrots
Pour batter into prepared pan, tap it against the counter to release any air bubbles.
Bake for 25 to 28 minutes, or until toothpick inserted in a few places comes out clean.
Cool completely before frosting.
To make frosting: in a large mixing bowl, beat cream cheese for 30 seconds. Add butter and beat for 2 minutes. Add powdered sugar, ¼ cup at a time, beating well after each addition. Beat in vanilla. Spread frosting on cake.
4 oz. cream cheese, 4 tablespoons unsalted butter, 2 cups powdered sugar, ½ teaspoon vanilla extract
Chill cake until ready to serve.
Notes
to measure out flour properly: fluff it with a fork or spoon in the container you store your flour in; then spoon it into the measuring cup, level out the top. Do not dip your measuring cup right into the flour. You will end up with too much of it and the cake won't be fluffy and moist.
grate carrots on small hole side of your grater
the cream cheese and butter should be very soft, as in you have to scrape it off the wrapper