First, get your pans and oven ready. Heat the oven to 350°F (175°C). Lightly grease the cake pans with vegetable oil and sprinkle in a little flour, shaking out the excess so nothing sticks.
In a mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt until well blended.
In another bowl, beat the sugar, eggs, and vegetable oil together until the mixture is smooth and creamy.
Add the grated carrots into the wet mixture and stir to combine. Then gently fold in the dry ingredients, mixing just until everything is blended. Stop as soon as you no longer see dry flour overmixing can make the cake heavy.
Divide the batter evenly between your two prepared pans. Place them in the oven and bake for 35 to 40 minutes, or until a toothpick pushed into the center comes out clean. Let the cakes rest in the pans for about 10 minutes before turning them out onto wire racks to cool completely.
While the cakes cool, make the frosting. Beat the softened cream cheese with the butter until silky and smooth. Slowly add the powdered sugar, a bit at a time, then mix in the vanilla extract. Keep beating until the frosting turns light and fluffy.
When the cakes are fully cooled, set one layer on a serving plate and spread a generous layer of frosting over the top. Place the second layer on top and frost the whole cake sides and all with the rest of the cream cheese frosting. Cut into slices and enjoy.