Preheat the oven to 350°F. Spray cooking spray in two 6-inch round cake pans (these are smaller than normal cake pans) and line with parchment paper on the bottom.
In a large mixing bowl, combine eggs, oil, applesauce, creamy peanut butter, carrot, banana, and honey. Whisk together until smooth.
Add flour and baking powder to the bowl and mix with a spoon. The mixture will be on the thick side.
Bake for 28 to 32 minutes or until a toothpick comes out clean when inserted into the middle of the cake.
Cool in the pan for 10 minutes, then remove and cool on a wire cooling rack. Let cool to room temperature before frosting cake. If frosted too early, the “frosting” will melt.
Once the cake is cooled, mix the Greek yogurt and peanut butter in a medium bowl with a hand mixer until light and fluffy, about 3 to 5 minutes.
Place the bottom layer of cake on a serving dish and place a generous amount of frosting on top and spread it out to the edges.
Layer with the other cake piece and frost top and sides of cake. Place dog bones on top of the cake for decoration.