Preheat the oven to 350 degrees Fahrenheit. Grease a 9 x 5 inch loaf pan with butter or non-stick cooking spray.
In a large mixing bowl, whisk together the flour, baking soda, salt, and cinnamon.
In a separate bowl, using a handheld or stand mixer fitted with a paddle or whisk attachment, beat the butter and brown sugar together on high speed for about 2 minutes or until smooth and creamy. Add the eggs one at a time, fully incorporating the first egg before adding the second. Add the yogurt, mashed banana, and vanilla, and mix over medium speed until well-combined.
With the mixer on low. slowly add the dry ingredients into the wet ingredients and mix until there are no floury pockets left. Do not over mix.
Pour the batter into the prepared loaf pan and bake for 55 to 60 minutes or until a toothpick inserted in the center of the loaf comes out clean. Check the loaf past the 30 minute mark, if the top and sides are getting too brown, loosely cover the pan with aluminum foil.
Remove from the oven and set the pan on a wire rack and allow the bread to cool completely before removing from the pan.