Preheat oven to 325°F and arrange the rack in the center. Lightly grease and flour a 9x5-inch loaf pan. Remove the peels and place the bananas in a small bowl. Thoroughly mash the bananas with a fork. Melt the unsalted butter and allow it to return back to room temperature.
Use a stand mixer fitted with the whisk attachment to beat together the brown sugar, granulated sugar, and eggs on medium speed until pale and fluffy, about 3–5 minutes.
Switch the mixer speed to low and slowly drizzle in the oil, then drizzle in the butter (making sure it’s cooled down from being melted). Add the mashed bananas, yogurt, and vanilla extract. Continue to mix at low speed until just combined.
In another large bowl, mix together the flour, baking soda, cinnamon, and salt.
Add all the dry ingredients to the wet ingredients and using a spatula (don’t use the mixer), gently fold in the dry ingredients until just combined. Don’t overmix; just fold until you don’t see any dry streaks.
Pour the batter into the prepared loaf pan. If desired, sprinkle the 2 tablespoons of brown sugar and 1 tablespoon granulated sugar evenly over the top of the bread.
Place the bread on a sheet pan. Bake for 50–70 minutes (wide variance depending on the pan you use, actual heat of the oven, humidity, etc.), until lightly golden brown on top, bread springs back when you press it, and a toothpick, when inserted in the center, comes out clean or with moist crumbs.
Remove the bread and allow it to cool in the pan for 8–10 minutes. Invert onto a cooling rack to finish cooling and slice with a sharp serrated knife.
Notes
Storage: Wrap the banana bread and keep it at room temperature for up to 3 days. You can put it in the fridge for longer storage. To freeze, cool the bread completely, then wrap it tightly and put it in a sealed container or bag in the freezer for 3 months.