Preheat oven to 350 degrees F (175 degrees C). Grease a 12-cup muffin tin or line cups with paper liners.
Beat eggs in a bowl. Mash bananas into the eggs. Add applesauce and vanilla extract.
Mix whole wheat flour, cane sugar, all-purpose flour, flax seeds, oats, white sugar, sea salt, and baking powder together in a bowl. Add banana mixture; stir to combine. Fold in chocolate chips and walnuts. Fill muffin cups.
Bake in the preheated oven until tops spring back when lightly pressed, about 25 minutes.