Preheat the oven to 350°F (175°C). Grease a 9x5-inch loaf pan and line with parchment paper.
In a large mixing bowl, mash the bananas until smooth. Add the eggs, melted butter, brown sugar, vanilla extract, and Greek yogurt, and whisk until well combined.
In a separate bowl, sift together the flour, baking soda, salt, cinnamon, and nutmeg. Gradually fold the dry ingredients into the wet ingredients until just combined — avoid overmixing.
If desired, fold in the walnuts or chocolate chips.
Pour the batter into the prepared loaf pan and smooth the top.
Bake for 55–65 minutes, until a toothpick inserted into the center comes out clean.
Let the bread cool in the pan for 10 minutes, then transfer to a wire rack to cool completely before slicing.