Preheat oven to 325 degrees and grease a 9x5 inch bread pan.
In a large bowl mix together mashed banana, Greek yogurt, applesauce, and sugar. Mix in vanilla and eggs.
Add flour, salt, baking soda and mix until just combined - DO NOT OVER MIX - just until there are no remaining streaks of flour. Pour into prepared pan.
Bake for 55-65 minutes, until top is browned and a toothpick inserted into the center of the bread comes out clean. Allow to cool completely on a wire rack before turning bread out of pan and slicing. Store in airtight container at room temperature up to 5 days.
In place of the applesauce you can sub an equal amount of oil (vegetable or canola) oil. The result will be equally moist, and a little more flavorful but also higher in calories - up to you!You can use less sugar if you want for a healthier version of this bread. I you want to use less sugar I recommend making sure to use VERY ripe bananas - the riper the bananas, the sweeter the bread will be.