Preheat the oven to 350°F/180°C. Grease or line an 8.5x4.5-inch or 9x5 inch loaf pan with parchment paper.
Let the butter melt in a small saucepan over medium heat. Once melted, let it cook for around 3-4 minutes until the milk solids have caramelized and the butter smells nutty. Pour the browned butter into a large heat-proof bowl and cool down for 10 minutes.
Mash the two bananas with a fork and add them to the cooled butter.
Add in the brown sugar, eggs, and vanilla. Whisk it well together until all combined.
Mix the flour, salt, and baking soda in a separate bowl.
Tip the dry ingredients into the wet ingredients and the yogurt and fold with a rubber spatula until well combined but not overmixed. You will see the brown flecks of butter throughout the batter.
Spoon the mixture into the prepared loaf pan.
Slice the extra banana lengthwise and place the sliced banana on top of the batter. Sprinkle with a bit of turbinado sugar.
Bake in the preheated oven for approximately 60-70 minutes or until the top of the bread springs back when touched and a skewer inserted into the center of the loaf comes out clean. If baking in a 9x5 inch pan it will need less time than a smaller pan.
Remove the baked banana bread from the tin and let it cool on a cooling rack for 20 minutes before slicing.
