Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a large bowl, mash the ripe bananas with a fork until smooth.
Add the brown sugar, unsweetened applesauce, and vanilla extract to the mashed bananas. Stir until well combined.
In a separate bowl, mix the rolled oats, ground cinnamon, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined.
Fold in the chopped walnuts evenly throughout the batter.
Using a tablespoon, scoop the dough onto the prepared baking sheet, spacing the cookies about 2 inches apart.
Flatten each cookie slightly with the back of the spoon.
Bake for 12 to 15 minutes or until the edges are golden and the cookies are set.
Remove from the oven and allow the cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.