Preheat your oven to 325 degrees F.
Spray two 9 inch by 5 inch round cake pans with non-stick cooking spray. An alternative method is to grease the pans with a light coating of butter or margarine, then cover with a very fine sprinkling of all-purpose flour.
In a medium bowl, sift together the flour, baking soda and salt.
In a large bowl mix together the softened butter and brown sugar with an electric mixer until the mixture is smooth and creamy.
Add the eggs and beat on low speed until well blended.
Add the bowl of dry ingredients to the bowl of wet ingredients and mix on low.
Scrape down the sides of the bowl with a spatula, then continue to mix until all ingredients are well blended.
Use a large mixing spoon to stir the banana, vanilla and walnuts or pecans (if you're using them) into the cake batter.
Pour the batter evenly between the two cake pans then place the pans in the pre-heated oven.
Bake for 40-50 minutes until cooked through. Test with a toothpick to make sure the batter is cooked through.
Remove the pans from the oven, using pot holders or oven mitts, then let cool on wire metal racks.
Cut each cake into 8 triangular pieces, for a total of 16 servings.
Optional: serve the banana cake with your favorite topping such as sweet butter, cream cheese, cream cheese frosting or even Nutella hazelnut spread.