In the mixer bowl, combine all wet ingredients and mix until well combined. Add the dry ingredients and mix on medium speed for 2 minutes. Fold in the shredded carrots.
Pour the batter into a greased 9×13-inch pan, spreading it out evenly.
Bake for 25-35 minutes, checking at the 25-minute mark with a toothpick to ensure it comes out clean. If needed, continue baking in 5-minute increments until done.
Remove the cake from the oven and let it cool on the counter for 1 hour.
Once completely cooled, frost the cake.
Cream Cheese Frosting:
Using the paddle attachment, beat cream cheese in the mixer on medium speed for 2 minutes.
Add butter and continue beating for another 2 minutes. Mix in vanilla extract followed by 1 cup of powdered sugar. Beat on low until all the powdered sugar is added and well mixed.
Increase the mixer speed to medium-high and beat for 4 minutes until the frosting is smooth and fluffy.