• Preheat oven to 325° F. Spray an 8x8 square dish with nonstick cooking spray and set aside.
  
• In a large bowl, combine flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Stir to combine and set aside.
  
• In a separate bowl, using a hand mixer or stand mixer, mix sugar, oil, and applesauce together. Add eggs, vanilla extract and mashed bananas and mix just until combined.
  
• Slowly incorporate the dry ingredients into the wet until just combined. Pour into prepared dish and bake 25-30 minutes or until toothpick comes out clean when inserted. Cool completely.
  

for the frosting-

• Place butter in a small saucepan over medium heat. As soon as the butter melts, remove from heat immediately and pour into a different container. Cool to room temperature.
  
• In a small bowl, using a hand mixer or stand mixer, whip together cooled melted butter, vanilla extract, powdered sugar and heavy cream until smooth and creamy.
  
• Spread over cooled cake and top with chopped walnuts, if desired.
  
• Slice into even squares and serve!