Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x5-inch loaf pan.

Stir sugar and melted butter together in a bowl. Mix in eggs, milk, and vanilla until well combined.

Combine sifted flour, cinnamon, baking soda, baking powder, and salt in a separate bowl. Stir flour mixture into butter mixture until smooth. Fold bananas and walnuts into the batter until fully incorporated. Spread batter evenly into the prepared pan.

Bake in the preheated oven until an instant-read thermometer inserted into the center of the loaf reads 195 degrees F (90 degrees C), about 55 minutes.

Remove from the oven and cool in the pan for 10 minutes. Remove loaf from the pan and finish cooling on a wire rack.