Preheat oven to 350°F. Grease an 8½ x 4½-inch loaf pan and set aside.
In a medium bowl, sift or whisk together flour, nutmeg, cinnamon, baking soda and salt. Set aside.
In a separate large bowl, whisk together mashed banana, melted butter, sugar, egg and vanilla extract.
Gradually add the dry ingredients to the wet ingredients, stirring just until combined. Fold in the walnuts.
Pour batter into prepared loaf pan. Bake until the bread is golden brown and a toothpick inserted in the center comes out clean, about 50-60 minutes. Do not overbake.
Remove from the oven, unmold from the pan, and cool completely on a wire rack before slicing and serving.