Preheat your oven to 350°F (175°C). Grease your cake pan or line it with parchment paper to prevent sticking.
Mix the dry ingredients. In a mixing bowl, combine the whole wheat flour and baking powder. Stir well to ensure the baking powder is evenly distributed.
Add the wet ingredients. Add the applesauce, peanut butter, vegetable oil, honey (if using), and egg to the dry ingredients. Mix until well combined. The batter should be thick and slightly sticky.
Fold in the grated carrots. Stir the grated carrots into the batter until they are evenly distributed. The carrots add moisture, sweetness, and a bit of texture that your dog will enjoy.
Pour the batter into the prepared pan. Smooth the top with a spoon to ensure even baking.
Bake for 25 minutes, or until a toothpick inserted into the center comes out clean. The cake should be golden brown and firm to the touch.
Cool the cake completely before serving. Allow the cake to cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely.
Frosting (optional): For a dog-friendly frosting, you can mix plain Greek yogurt with a bit of peanut butter or mashed sweet potato. Spread it over the cooled cake.
Serve and celebrate! Cut the cake into appropriate-sized slices based on your dog's size and dietary needs. Store any leftovers in the refrigerator for up to 5 days.