Preheat oven to 350°F. Grease the bottom and sides of a 9x5x3” loaf pan and set aside.
Combine eggs, sugar, bananas and oil in a mixer and mix well.
Add baking powder, baking soda, cinnamon, salt, and flour, and blend well until just moistened. Transfer mixture to baking pan.
For optional streusel nut topping, combine ¼ cup packed brown sugar and 3 tablespoons all-purpose flour. Cut in 2 tablespoons butter until mixture resembles coarse crumbs. Stir in 1/3 cup chopped walnuts.Sprinkle on top of the batter mixture.
Bake in a 350°F oven for 55 to 60 minutes or until a wooden toothpick inserted near the center comes out clean. If necessary, cover loosely with foil for the last 15 minutes of baking to prevent over browning.
Cool in a pan on a wire rack for 10 minutes.Remove from pan. Cool completely on a wire rack. Wrap and store in an airtight container overnight if desired.