Step 1: Preheat your oven to 350°F (175°C).
Step 2: Grease your 9x5-inch loaf pan with melted butter.
Step 3: In a medium bowl, whisk together flour, baking powder, baking soda, salt, and nutmeg. Set aside.
Step 4: In a large bowl, beat the eggs and add sugar. Mix well, then add mashed bananas and melted butter, stirring until blended.
Step 5: Gradually add the dry mixture to the wet mixture, folding gently until just combined.
Step 6: Pour the batter into the prepared loaf pan and smooth the top. Bake for 60-70 minutes, or until a toothpick inserted comes out clean.
Step 7: Let the banana bread cool in the pan for 10 minutes, then transfer to a wire rack to cool completely. Slice and enjoy!