Whisk together the salt, baking soda, and all-purpose flour.
In a separate bowl, whisk together the Greek yogurt, mashed banana, melted butter, eggs, vanilla extract, and brown sugar.
Add the dry ingredients to the wet and mix until just combined using a rubber spatula.
Pour the batter into a greased loaf pan, and smooth out the top.
Bake the banana bread at 350 degrees for 45-55 minutes, until a toothpick inserted comes out clean.
Allow the banana bread to cool for 10 minutes in the pan, then remove it onto a wire cooling rack to cool completely.