Preheat your oven to 350°F (175°C).
In a large bowl, whisk together the eggs, vegetable oil, applesauce, brown sugar, granulated sugar, and vanilla extract until well combined.
In another bowl, mix the flour, salt, baking powder, baking soda, cinnamon, and shredded carrots.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
If you’re using chopped pecans, fold them in at this stage.