Preheat oven to 350 degrees F.
In a large bowl, combine flour and baking soda.
In a separate bowl mix together vegetable oil, peanut butter, applesauce and pumpkin puree. Once combined, mix in egg and mix until combined.
Combine wet and dry ingredients and stir until combined.
Pour mixture into an 8" round pan (a square pan can also be used) that has been greased with oil.
Bake for approximately 25-30 minutes or until a toothpick inserted into the center comes out clean and the cake springs back when pressed lightly.
Allow to cool on a wire rack prior to removing from pan.
After cooling, add frosting if desired.