Cake:
Frosting:
Position a rack in the middle of the oven. Preheat the oven to 350 °F (176 °C).
Grease two 9-inch round cake pans, line the bottom with parchment paper, and then grease the top. Or grease and flour the bottom and sides of both pans.
Whisk flour, baking soda, salt, cinnamon, ginger, nutmeg, and cloves in a medium bowl until very well blended.
In a separate bowl, whisk the oil, brown sugar, and vanilla.
Add the eggs, one at a time, whisking after each one.
Switch to a large rubber spatula. Scrape the sides and bottom of the bowl, then add the dry ingredients in three parts, gently stirring until they disappear and the batter is smooth.
Stir in the carrots.
Divide the cake batter between the prepared cake pans.
Bake until the tops of the cake layers are springy when touched and when a toothpick inserted into the center of the cake comes out clean, 35 to 45 minutes.
Cool the cakes in the pans for 15 minutes, then carefully turn the cake layers out onto cooling racks. Remove the parchment paper and cool completely. If you find that a cake layer is sticking to the bottom of the pan, leave the cake pan upside down and allow gravity to do its thing.
In a large bowl using a handheld or stand mixer fitted with a whisk or paddle attachment, beat the cream cheese and butter together on medium-high speed until smooth, about 2 minutes.
Add the confectioners’ sugar, vanilla extract, and a pinch of salt. Beat on low speed for 30 seconds, then increase to high speed and beat for 3 minutes until completely combined and creamy. Add more confectioners’ sugar if frosting is too thin, a little milk if frosting is too thick, or an extra pinch of salt if frosting is too sweet. Frosting should be soft, but not runny.
First, using a large serrated knife or cake leveler, layer off the tops of the cakes to create a flat surface.
Place 1 cake layer on your cake turntable, cake stand, or serving plate. Evenly cover the top with frosting.
Top with 2nd layer, more frosting, and then top with the 3rd layer. Spread remaining frosting all over the top and sides.
Refrigerate cake for at least 15-20 minutes before slicing. This helps the cake hold its shape when cutting.
Cover leftover frosted cake tightly and store in the refrigerator for up to 5 days.
