Preheat oven to 350°F and grease a sheet pan (18" x 13").
In a mixing bowl, stir together the flour, baking powder, baking soda, salt and cinnamon; set aside.
In a stand mixer or large mixing bowl, combine the oil, sugar, brown sugar, eggs, applesauce and vanilla; add the shredded carrots and mix well.
Add the dry ingredients to the wet ingredients and mix until just combined (don't overmix).
Pour into prepared sheet pan and spread evenly.
Bake for 24-28 minutes, or until a toothpick in the center comes out clean. (A few moist crumbs are fine, but you don't want it to be gooey). Let cool completely.
Make the frosting: Beat the cream cheese and butter until fluffy. Beat in the powdered sugar and vanilla until smooth.
Spread the frosting over the cooled carrot cake. Decorate with sprinkles, pecans, or little candy carrots.
Store the finished cake in the refrigerator.