Preheat the oven to 350°F (175°C). Lightly grease a 9 × 5-inch loaf pan and line it with parchment paper, leaving enough overhang to lift out the loaf.
Place the bananas in a large bowl and mash them with a fork.
Add the eggs, brown sugar, oil, Greek yogurt, applesauce and vanilla. Whisk until well combined.
In a separate bowl, whisk together the flour, baking soda, baking powder, cinnamon and salt.
Add the dry ingredients to the banana mixture. Fold gently with a spatula just until no dry streaks of flour remain.
Fold in the chocolate chips or nuts, if using.
Transfer the batter to the prepared loaf pan and smooth the top.
Bake for 50 to 60 minutes, or until a skewer inserted in the center comes out without wet batter. A few moist crumbs are perfectly fine.
Let the banana bread cool in the pan for 15 minutes.
Use the parchment paper to lift it from the pan, then transfer it to a wire rack. Allow it to cool for at least another 30 minutes before slicing.