Preheat oven to 350°F (175°C).
Grease an 8½ x 4½-inch loaf pan and set aside.
In a medium bowl, whisk together flour, nutmeg, cinnamon, baking soda, and salt.
In a large bowl, whisk mashed bananas, melted butter, sugar, egg, and vanilla extract until smooth.
Gradually add the dry ingredients to the wet ingredients.
Stir gently until just combined. Do not overmix.
Fold in the chopped walnuts.
Pour the batter into the prepared loaf pan and smooth the top.
Bake for 50–60 minutes, until golden brown and a toothpick inserted in the center comes out clean.
Remove from the oven and carefully unmold from the pan.
Let cool completely on a wire rack before slicing.