Position rack in center of oven and preheat to 350°F. Butter or spray a 9"x 5" loaf pan, set aside
In a large bowl whisk together banana, brown sugar, yogurt, melted butter, eggs and vanilla.
In a separate bowl, whisk together flour, baking powder, baking soda and salt.
Whisk the dry ingredients into the wet in 2 additions, mixing only until the dry is just incorporated. It's better to under-mix slightly then over-mix.
Pour batter into greased loaf pan and bake for 50 minutes. to 1 hour or until tester comes out clean.
Let cool in pan for about 10 minutes and then turn out onto a cooling rack.