Preheat your oven to 350°F (175°C). Lightly grease and flour a small cake pan (about 6 inches).
In a medium bowl, whisk together the whole wheat flour and baking soda. If using, stir in shredded carrots or pumpkin puree.
In a separate bowl, combine the unsweetened applesauce, xylitol-free peanut butter, water (or almond milk), and egg. Mix until well combined.
Pour the wet ingredients into the dry ingredients and stir until just combined. Be careful not to overmix.
Pour the batter into the prepared cake pan and spread evenly.
Bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for about 10 minutes before inverting it onto a wire rack to cool completely.
While the cake cools, prepare the frosting. In a small bowl, mix the Greek yogurt and peanut butter until smooth and creamy.
Once the cake is completely cool, spread the frosting evenly over the top. You can add a few dog-safe sprinkles or a small dog biscuit on top for decoration if desired.