Preheat the oven to 350 degrees Fahrenheit. Line the bottoms of two 8-inch springform cake pans with parchment paper rounds.
In a large mixing bowl, whisk together the eggs, oil, applesauce, lemon juice, brown sugar, and vanilla extract until everything is well-combined any any lumps of brown sugar have dissolved.
Whisk together the dry ingredients (gluten-free flour, baking powder, baking soda, ground cinnamon, ground ginger, and sea salt) in a separate large bowl until combined. Pour the wet ingredients into the bowl with the dry ingredients and mix until combined and a thick cake batter forms.
Mix in the shredded coconut, raisins, grated carrot, and chopped pecans (or walnuts) until well-distributed throughout the batter.
Evenly divide the cake batter between the two prepared cake pans and spread it into an even layer.
Bake on the center rack of the preheated oven for 32 to 40 minutes, or until the cake tests clean. Mine take about 38. To verify the cake is cooked through, you can insert a toothpick into the center of the cake and make sure it comes out clean. Cakes are considered fully cooked when they reach an internal temperature of at least 190 degrees F, so you can use an instant read thermometer to test the temperature of the inside of the cake as well (this is what I do).
Remove the cakes from the oven and allow them to cool completely to room temperature.
Once you’re ready to frost the cakes, release them from their molds and discard the parchment paper.
Place one cake on a cake stand (or the serving dish you’re using), and frost the top with cream cheese frosting.
Place the second cake on top of the cream cheese layer and frost the full outside of the cake with the remaining frosting.
If you’d like to decorate the cake with chopped nuts and/or shredded coconut, feel free to get creative.
Slice and serve.