Preheat oven to 325 degrees. Line a 9 x 5 loaf pan with parchment paper and set aside.
In a large bowl, combine flour, baking soda, salt and cinnamon. Set aside.
Brown butter in a medium saucepan over medium-low heat stirring constantly with a wooden spoon until the butter gets foamy and releases a nutty aroma (approx. 7 minutes).
Once browned bits begin to form on the bottom, remove pan from the heat.
Stir in rum and brown sugar then set aside to cool for 10 minutes.
In a separate bowl, whisk mashed bananas and beaten eggs with vanilla extract until combined.
Pour the cooled brown butter rum mixture into the mashed banana mixture. Stir until incorporated.
Add flour mixture to wet ingredients, one cup at a time, gently stirring until just combined. Avoid overmixing or bread will be dry.
Spoon batter into loaf pan then level with a spatula.
Slice remaining banana in half lengthwise then press each half onto the top of the batter.
Brush banana halves with a pinch of brown sugar then bake for 1 hour or until a toothpick inserted into the center of the loaf comes out clean. Tent bread with foil while it bakes if it appears to be overbrowning.
Cool bread in the pan for 10 minutes before turning loaf out onto a baking rack to cool completely.
Bread can be stored in an airtight container at room temperature up to 2 days or in the refrigerator up to 7 days.
