Preheat the oven to 350 degrees F. Grease an 8 1/2 by 4 1/2 inch baking pan and set aside.
In a large bowl mash the bananas with a fork or pastry blender.
Stir in the the butter, eggs, yogurt, and vanilla.
Add the flour, sugar, baking powder, baking soda, and salt to the bowl and stir to combine.
Don't over mix. The batter should be thick and a little chunky
Scrape the batter into the greased pan and bake until golden brown and a toothpick comes out clean, about 55 minutes.
Let the banana bread cool in the pan for 10 minutes and then remove it from the pan and let it cool on a wire rack for at least 1/2 before serving.
Notes
This recipe is actually really flexible! You can use whole wheat flour instead of the white (or half and half), you can use sour cream instead of the yogurt, and I have even had great luck making "flax eggs" instead of using real eggs for this recipe (mix 1 tablespoon ground flax meal with 2.5 tablespoons water PER egg you need, stir and let it rest for 5 minutes before using). You can also sub oil for the butter. Use what you have on hand and what's easiest for you.
You can also add 1-2 teaspoons of cinnamon to the batter or 1 cup of chocolate chips if you'd like.
You can reduce the sugar in this recipe to 1/2 cup if you like a less sweet banana bread.
Really brown bananas are the best for banana bread. You can easily freeze them if you don't have time to bake.