Before baking, let's make sure the oven is ready! Start by preheating the oven to 350 degrees Fahrenheit (175 degrees Celsius). Then, take an 8-inch round cake pan and coat it with cooking spray.
Next, in a large mixing bowl, combine flour, white sugar, brown sugar, baking soda, baking powder, cinnamon, pumpkin pie spice, and salt. Whisk all the ingredients together until they are well combined.
it's time to prepare the egg whites and vanilla extract. In a separate small bowl, beat the two ingredients together using an electric mixer until they become fluffy and light.
For the carrot, place them in a food processor and pulse them until they are finely grated. Be careful not to turn them into a pulp, which can make the cake texture undesirable.
Afterward, mix the carrots and applesauce into the flour mixture. Stir well until everything is thoroughly combined. Then, add the egg white mixture and fold it into the batter until it's well incorporated.
Now it's time to put the batter into the prepared cake pan. Spoon it in evenly and spread it out to make sure the cake bakes evenly. Bake in the preheated oven for 27 to 30 minutes, or until a knife inserted into the center comes out clean, and the cake is pulling away from the sides of the pan.Finally, take the cake out of the oven and let it cool completely on a wire rack. Once it's cool, it's ready to be served!