Preheat oven to 175 °Celsius.
Peel and measure the bananas. Mash them until fine with a fork. Set aside.
Grease and flour a loaf tin measuring 8 inches by 4 inches.
Sift flour, salt, baking powder and baking soda together. Set aside.
In a separate bowl, beat butter, brown sugar till light and fluffy (approximately 2 minutes)
Add egg and continue to beat until the egg is well incorporated into the creamed mixture.
Fold in the sifted flour mixture into the creamed mixture alternately with the buttermilk, starting and ending with the flour.
Add vanilla extract and mix again for a few seconds.
Finally, add the mashed bananas into the cake batter and mix to spread the banana evenly into the cake batter.
Pour batter into the prepared loaf tin and bake at 175°Celsius for 40 to 45 minutes until cake is done and firm to the touch. Test the cake at 35 minutes by inserting a skewer in the center of the cake. If it comes out without any wet batter, it is ready and can be removed from the oven. If not, continue baking and test again after a few minutes.
Remove the cake from the oven and let it rest on a wire rack for 2 to 3 minutes before loosening the sides with a palette knife and turning it over onto the wire rack.
Turn the cake over (facing upright) and let it cool down until it is slightly warm to the touch. Wrap the cake in cling wrap and refrigerate until it cools down completely.
Bring the cake to room temperature before serving.