Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking pan or line it with parchment paper.
In a large mixing bowl, whisk together the almond flour, oat flour, baking powder, baking soda, cinnamon, nutmeg, ginger, and salt (if using).
In a separate bowl, beat the eggs, then mix in the unsweetened applesauce, sugar-free maple syrup (or sweetener), melted coconut oil, and vanilla extract.
Gradually add the wet ingredients to the dry ingredients, stirring until just combined.
Fold in the grated carrots, chopped nuts (if using), and shredded coconut (if using).
Pour the batter into the prepared baking pan and spread it evenly. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool completely in the pan before frosting.
In a mixing bowl, beat the softened cream cheese and butter until smooth and creamy.
Add the sugar-free powdered sweetener and vanilla extract, and beat until well combined. If the frosting is too thick, add a splash of unsweetened almond milk to reach your desired consistency.
Once the cake is completely cool, spread the frosting evenly over the top. Garnish with chopped nuts and a sprinkle of cinnamon.
Slice and serve at room temperature. Store any leftovers in the refrigerator for up to 5 days.