Preheat & Prepare: Preheat oven to 350°F (175°C). Grease and flour, or coat with non-stick spray, two 9x5 inch loaf pans.
Combine Wet Ingredients: In a large bowl, using an electric hand mixer or stand mixer, blend the melted butter and brown sugar. Beat in the vanilla and eggs one at a time. Gently stir in the mashed bananas.
Add Dry Ingredients: In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add this dry mixture to the wet ingredients, mixing on low speed or by hand until just combined. Do not overmix; a few flour streaks are okay.
Fill Pans & Top: Divide the batter evenly between the two prepared loaf pans. Sprinkle the tops of both loaves generously with extra brown sugar.
Bake: Bake for 55-70 minutes. Start checking for doneness around 55 minutes. Insert a toothpick into the center of each loaf; it should come out clean or with a few moist crumbs. Loaves may not finish at the exact same time, so check both. If tops brown too quickly, loosely tent with foil.
Cool: Let the loaves cool in their pans on a wire rack for 10-15 minutes before carefully inverting them onto the rack to cool completely before slicing.