Preheat the oven to 350°F (175°C). Grease a 9x5-inch loaf pan and line with parchment paper for easy removal.
In a medium bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Set aside.
In a large bowl, mash bananas until mostly smooth. Add melted butter, sugar, eggs, and vanilla; whisk until combined.
Add dry ingredients to wet and fold gently until nearly combined. Fold in chopped apple and nuts, if using. Do not overmix.
Pour batter into prepared pan, smooth the top, and sprinkle with cinnamon-sugar if desired. Bake 55–65 minutes, tenting with foil if the top browns too quickly, until a toothpick comes out with a few moist crumbs.
Cool in the pan for 10 minutes, then remove to a rack to cool completely. Slice and enjoy warm or at room temperature.