Preheat the oven to 350°F (180°C). Spray two 9-inch round cake pans well with non stick cooking spray and line the bottom of each pan with a parchment paper circle.

In a large mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt until well combined. Set aside.

In a separate large mixing bowl, whisk together the oil, eggs, brown sugar, granulated sugar, applesauce, and vanilla extract until fully combined. Add the grated carrots to the wet ingredients and mix until well combined.

Pour the wet ingredients into the dry ingredients and mix until just combined, being careful not to over mix.

Pour the cake batter evenly between both prepared cake pans. Bake for 30 to 35 minutes or until a toothpick inserted comes out clean.

Remove from the oven, cool in the pans for 20 to 25 minutes. Then transfer to a wire rack to cool completely.

To make the frosting, beat the cream cheese until smooth, then add the butter and mix until well combined.

Add in the powdered sugar and vanilla extract and mix until fully combined.

Level off the cakes, apply frosting between layers, and then frost the cake as desired.