Preheat the oven to 325 degrees F (165 degrees C). Line a baking sheet with parchment paper.
Mix flour, bananas, ½ cup sugar, butter, walnuts, egg, baking soda, and salt together in a bowl until well combined. Drop 3-tablespoon portions dough onto the prepared baking sheet, about 2 to 3 inches apart. Sprinkle remaining 1 tablespoon sugar over cookies.
Bake in the preheated oven until golden brown and edges are set, 15 to 20 minutes.
