Preheat the oven to 350˚F and line a 9 by 5-inch loaf pan with parchment paper, leaving excess on the two longer sides.

Mash the bananas in a large bowl. Add sugar and butter, and continue to mash with the bananas until almost completely smooth.

Add the eggs and vanilla and whisk until smooth. Add flour, baking soda, cinnamon and salt, and fold with a rubber spatula until no streaks of flour remain.

Scrape the batter into the prepared pan and bake for 50 to 55 minutes, or until a cake tester inserted in the center of the loaf comes out clean.

Let cool for at least 20 minutes, then remove from pan and cool completely on a wire rack before slicing and serving.