Make the waffles: In a medium bowl, mix together the flour, sugar, baking powder, baking soda, salt, cinnamon and nutmeg.
In a separate bowl, using a mixer fitted with the whisk attachment, whip the eggs until they are light in color and air has been incorporated. They should double in size.
Add the mashed banana and whip for another minute.
Make a well in the center of the dry ingredients and add the milk, oil and vanilla.
Mix just until combined, then fold into the banana mixture.
Use a waffle iron to cook the waffles according to the manufacturer's instructions, but leave slightly underdone if you're planning on freezing them.
Make the syrup: Heat the peanut butter and maple syrup together in a small saucepan over low heat. Stir to incorporate. Remove when incorporated and warmed. Serve with banana spice waffles.