Preheat oven to 350°F (175°C) and grease a 9x5-inch loaf pan.
In a large mixing bowl, whisk together the mashed bananas, melted butter, brown sugar, egg, vanilla, and instant espresso powder until well combined.
In a separate bowl, whisk the flour, oats, baking soda, and salt.
Gradually fold the dry ingredients into the wet ingredients until just combined, being careful not to overmix.
Fold 1/2 cup of chopped walnuts into the batter.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Sprinkle the remaining 1/4 cup of chopped walnuts evenly over the batter surface.
Bake for 60 to 65 minutes, or until a toothpick inserted into the center comes out clean.
Remove from oven and allow the bread to cool in the pan for 10 minutes.
Transfer the loaf to a wire rack to cool completely before slicing.