To make the cake: Preheat the oven to 325 degrees F. Line a 1-inch rimmed baking sheet (13 x 18 x 1 inches) with parchment paper. Brush the parchment and sides of the baking sheet with about a teaspoon of coconut oil or spray with cooking spray. Set aside.
In a large bowl, whisk together the flour and baking soda. Add the peanut butter, honey, oil, eggs, and water. Mix until completely combined and then fold in the shredded apples. Pour the dough onto the lined baking sheet and spread it out into one even layer. A spatula is pretty handy.
Transfer to the oven to bake for 15 to 17 minutes, or until the top is lightly golden brown and springs back when touched.
To make the frosting: In a medium bowl, whisk together the Greek yogurt and honey.
To toast the coconut: Add to a small skillet, set over medium-low heat, cook until lightly golden brown, moving the pan every now and then to ensure even toasting.
To assemble the cakes: Using a 4-inch round cutter, stamp out a series of small cakes. I got about 12 from my baking sheet. (Save the scraps for treats! Should be good for 1 week when put into a Ziplock bag and stored in the fridge.) Stack the cakes in threes or twos. Top with a dollop of "frosting" and a sprinkling of coconut flakes. Insert candles and party on!