Preheat your oven to 350 degrees Fahrenheit (175 degrees Celsius) and prepare a 12-cup muffin tin with paper liners. Set aside.
In a large bowl, whisk together the peanut butter, mashed banana, applesauce, brown sugar, eggs, vanilla and oil until smooth and well combined.
Add the all purpose flour, oats, baking soda, and salt, and toss them gently together with a fork before incorporating them into the wet mixture.
Using a silicone spatula, mix everything together until no streaks of flour remain. Don't over-mix but be sure all the flour is incorporated.
Divide the batter evenly between the prepared muffin cups about 3/4 full or more. This is a thick batter, so they shouldn't overflow.
Bake at 350 degrees Fahrenheit (175 degrees Celsius) until the muffins lose their shine on top and a toothpick inserted into the middle of one of the muffins comes out clean.
Let them cool in the tins for several minutes before removing them to a wire cooling rack to cool completely.