Preheat the oven to 350. Grease a loaf pan (9 X 5 inches) with cooking spray or butter.
Place butter in a small skillet or sauce pan and melt it on medium-low heat. Swirl the pan around as the butter begins to foam. The foam will subsides and the butter will begin to brown. When it begins to smell nutty and the butter turns a shade of golden brown, remove from heat immediately. Don't let it burn; let cool.
In a large bowl, whisk the flour, sugar, baking soda, salt, ginger and cinnamon.
Place slightly beaten eggs in a seperate bowl. Add the mashed bananas, yogurt (or milk), the cooled brown butter and vanilla and stir to mix well.
Pour the banana mixture into the flour mixture and stir gently with a rubber spatula until just combined; do not over mix. Scrape batter into the prepared pan, smooth the top; bake preheated oven for 50 - 60 minutes, or until a tester comes out clean. (Depending on many factors, this may take longer, but not so long as to dry out cake.).
Cool the loaf in the pan on a rack for 5 minutes then tip out on to the rack and let cool completely before slicing.