Preheat oven to 350°F (176°C). Line three 8 or 9-inch round cake pans with parchment paper then grease with cooking spray. Set aside.
Measure out milk then stir in white vinegar. Set aside.
In a separate large bowl, measure out and whisk together dry ingredients then create a well in the center. In the middle of the well, pour in the milk-white vinegar mixture, oil, and vanilla. Stir until just incorporated and then stir in grated carrots.
Divide the batter evenly between cake pans. Smooth the tops then bake for 15-20 minutes or until set.
Cool the cakes in their pans until just warm. Flip the cakes over onto cooling racks, remove the parchment paper and cool completely.
While the cakes are cooling, make the cream cheese frosting.
Use a serrated knife to level off the tops of the cakes (if desired). Stack carrot cakes with frosting in between. With remaining cream cheese frosting, cover the sides and top.
Decorate with chopped nuts, shredded coconut or colored frosting carrots.