Preheat your oven to 350°F (175°C).
Grease and line three 8-inch round cake pans with parchment paper.
In a large bowl, whisk together the flour, sugar, baking powder, baking soda, cinnamon, nutmeg, ginger, and salt.
In another bowl, mix the applesauce, plant-based milk, melted coconut oil, and vanilla extract.
Add the wet ingredients to the dry ingredients, stirring until just combined.
Fold in the grated carrots.
Divide the batter evenly among the three prepared pans and spread it out evenly.