Step 1: Preheat your oven to 350°F (175°C). Lightly grease and flour a 9x5-inch loaf pan, or line with parchment paper.
Step 2: In a large bowl, mash the ripe bananas with a fork until mostly smooth but with a few small lumps remaining. Stir in the lightly beaten eggs, granulated sugar, melted butter, and vanilla extract until well combined.
Step 3: In a separate medium bowl, whisk together the all-purpose flour, baking soda, ground cinnamon, ground nutmeg, and salt.
Step 4: Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix; a few lumps are fine. Fold in the chopped walnuts or pecans.
Step 5: Pour the batter into the prepared loaf pan and spread evenly. Bake for 50-60 minutes, or until a wooden skewer or toothpick inserted into the center comes out with moist crumbs (not wet batter).
Step 6: Let the banana bread cool in the pan for 10-15 minutes before carefully inverting it onto a wire rack to cool completely before slicing and serving.