Pb carrot cake for dogs

Cake
1 egg or 3 tbsp applesauce
1/4 cup peanut butter
1/4 cup oil
1 tsp vanilla extract
1/4 cup sugar
1 tsp baking soda
1 cup flour
1 cup shredded carrots
Bake at 330° for 40 minutes, let cool.
Frosting
1/4 cup corn/ tapioca starch
1/2 cup peanut butter(creamy)
1 cup Greek yogurt
1 tsp vanilla extract