Prep oven: Preheat the oven to 350°. Coat an 8" x 8” square baking dish with cooking spray.
Toast walnuts: Spread the walnuts on an ungreased baking sheet or stone and toast in oven for 5 to 8 minutes, or until toasty and fragrant.
Mix wet ingredients: While the walnuts are toasting, mash the bananas in a medium sized bowl. Add the remaining wet ingredients: oil, apple sauce, sugar, and vanilla extract. Mix until smooth.
Combine dry ingredients: In a large mixing bowl, combine the dry ingredients: oats, flour, baking powder, salt, cinnamon, nutmeg, and baking soda. Add the banana (wet) mixture and stir until just combined. Fold in the toasted walnuts and raisins, being careful not to overmix.
Bake: Pour the mixture into the prepared pan and spread evenly. Bake for 25 to 30 minutes, or until the top is browned and a toothpick inserted comes out nearly clean. Allow to cool completely before cutting into bars.