Preheat your oven to 350 degrees Fahrenheit and prepare a 12-cup muffin tin with paper liners (or grease very well with butter or cooking spray if you prefer not to use paper liners). Mash the bananas in a large bowl and mix in the sugar and egg with a wooden spoon until well blended.

Add the vegetable oil and mix well. Add the flour, baking powder, baking soda, salt, cinnamon and nutmeg, along with 3/4 cup of the chopped walnuts. Adding the walnuts with the dry ingredients helps prevent over-mixing.

Mix everything together just until the flour disappears and the walnuts are distributed evenly throughout the batter. In a small bowl, combine the remaining 3/4 cup walnuts, brown sugar and melted butter and mix until the walnuts are coated.

Bake for about 20-23 minutes, or until the muffins are golden brown on top and a toothpick inserted into the center of one of the muffins comes out clean. Let the muffins cool in their tins for a few minutes before removing them to a wire rack to cool completely.