For a first birthday or a family celebration, this Apple Cake is easy and delicious. (Note: You'll want to start the frosting the night before you plan to make the cake so it has time to thicken.)
Preheat oven to 350 degrees F and grease two 6-inch round cake pans with nonstick spray. Trace the pans onto parchment paper and cut out. Place parchment into the cake pans, trimming as needed to fit. Coat again with nonstick spray.
Stir together the eggs, butter, applesauce, maple syrup, vanilla, and diced apple. Gently fold in the flour, cinnamon, baking powder, baking soda, and salt.
Divide batter between the two pans. (I put 1 cup into each, then divide the rest evenly by eye.) Spread the batter evenly in the pan with a spatula.
Bake for 26-28 minutes, or until the cakes are lightly golden brown around the edges, firm to the touch, and a cake tester inserted into the center comes out evenly. Let cool in the pans for about 5 minutes, then invert to cool completely on a wire rack.
To make the frosting:
Place a fine mesh strainer over a bowl. Line strainer with cheesecloth or two layers of paper towels. Place the yogurt on top of the paper towels on top of the cheesecloth or paper towels in the strainer. Cover and store overnight in the fridge. Liquid will come out of the yogurt making it thicker. (About 1/4 cup of liquid was in the bottom of the bowl each time I made it; discard this.)
Add the yogurt (spoon it off of the strainer) to a bowl with maple syrup and vanilla extract. Stir well with a wooden spoon or beat with a hand held electric mixer.
To assemble the cake:
Place one cake on a platter or cake plate. Top with 1/2 cup of the frosting and spread evenly.
Add the second cake on top, pressing down gently. Spread the remaining frosting on top.
Notes
Dice the apple finely to about the same size. You don't have to peel it.
Dairy-Free: Use coconut oil instead of butter to make this cake dairy-free. You'll also want to use nondairy Greek yogurt.
Egg-Free: Omit the egg. Increase the applesauce to 3/4 cup and bake for 32-34 minutes. Let cool fully in the pans.
You can make the cake a day ahead. Let cool, then store in an airtight container at room temperature. Frost just before serving if possible.
Double the frosting recipe if you want to frost the sides of the cake too.