Preheat oven to 350°F
Whisk the wet ingredients in a large bowl.
Add in the flour and baking soda and stir until well combined. It will be a thick consistency.
If you want to add the shredded carrots, fold them into the batter.
Split the batter into two greased 4" cake pans. Because it's a pretty thick batter, you may need to shake the pans on the counter to level it out.
Bake for 25-30 minutes, or until a toothpick comes out clean.
Let the cakes cool for a few minutes and flip them onto a cooling rack to completely cool before icing
To make icing: mix greek yogurt and peanut butter
Assembly: Place one of the cooled cakes onto final plate/stand, and ice the top with half of the icing. If cake has a very round top, you may need to cut the top off to make it flat for top piece to sit on. Then place the other cake on top and ice the top with the rest of the icing. Add some dog treats on top or lining the edges.
Serve: Depending on your dog's size, you may want to slice the cake into several servings. (We give each of our large dogs a quarter serving at a time)