Preheat your oven to 350°F (175°C). Lightly spray two 5-inch cake pans with olive oil.

In a medium mixing bowl, whisk together the eggs and brown sugar until fluffy and light in color.

Gently fold in the Greek yogurt and applesauce into the egg mixture until well integrated.

In a separate bowl, whisk together the flour, baking powder, cinnamon, and ginger until evenly mixed.

Slowly add the dry ingredients into the wet mixture, stirring gently until just combined.

Fold in the grated carrots and optional raisins and walnuts, mixing until evenly distributed.

Pour the batter into the prepared cake pans and bake for 15-20 minutes until a toothpick comes out clean.

Let the cakes cool in the pans for about 10 minutes, then transfer them to a wire rack to cool completely.

Once cooled, frost the top of one layer with frosting, stack the second layer, and frost the top and sides as desired.