Step 1

Make the cake: Arrange a rack in the middle of the oven and heat to 350°F. Coat a 9x13-inch baking dish with cooking spray; set aside.

Step 2

Place the flour, cinnamon, baking powder, baking soda, and salt in a medium bowl and whisk to combine. Place the eggs and vanilla in a medium bowl and whisk to combine; set both bowls aside.

Step 3

Place the sugar and oil in a the bowl of a stand mixer fitted with the paddle attachment. (Alternatively, use an electric hand mixer or whisk and large bowl.) With the mixer on low (or by hand), beat 1/3 of the flour into the sugar mixture. Beat in 1/3 of the egg mixture. Continue adding the flour and eggs in alternating additions. Stop mixing when the last of the flour is just barely incorporated. Add the carrots and fold them in by hand with a rubber spatula, working slowly and gently until the carrots are distributed and no more dry flour remains.

Step 4

Pour the batter into the baking dish and gently tap the dish a few times against the counter to work out the air bubbles. Bake for 25 minutes. Rotate the baking dish 180 degrees, then bake until the cake is slightly puffed in the middle and browned on the edges, and a toothpick inserted in the middle should come out clean, 20 to 25 minutes more.

Step 5

Place the cake on a wire rack and let cool completely before frosting, about 1 hour. You can also cover the cooled cake with plastic wrap and store at room temeperature to frost the next day.

Step 6

Make the frosting: Place the cream cheese and butter in the bowl of a stand mixer fitted with the paddle attachment. (Alternatively, use an electric hand mixer and large bowl.) Beat on medium speed until combined. Gradually beat in the powdered sugar, vanilla, and salt until the frosting starts to come together into lumps. Increase the speed to to high and continue to beat until fluffy and creamy, scraping down the sides of the bowl as needed. Dollop the frosting over the cake and spread into an even layer.