Preheat your oven to 350°F (175°C). Grease your 9x13 inch baking pan or line it with parchment paper for easy removal.
In a saucepan over medium heat, melt the unsalted butter, stirring frequently until it turns golden brown and has a nutty aroma. This should take about 5-7 minutes. Remove from heat and let it cool slightly.
In a large mixing bowl, whisk together the egg, light brown sugar, liquid-state coconut oil, sour cream, vanilla extract, and mashed ripe bananas until smooth.
In another bowl, combine the all-purpose flour, baking powder, baking soda, and optional salt. Stir to mix.
Gradually add the dry ingredients to the wet mixture, folding gently until just combined. Be careful not to overmix; a few lumps are okay.
Pour the batter into the prepared baking pan, spreading it evenly. Bake for 25-30 minutes or until a toothpick inserted in the center comes out clean. Allow the bars to cool in the pan for about 10 minutes, then transfer to a cooling rack.
While the bars are cooling, make the vanilla bean browned butter glaze. In a medium bowl, whisk together the browned butter, confectioners sugar, vanilla bean paste, and optional salt. Gradually add cream or milk until you reach your desired consistency.
Once the banana bread bars are completely cool, drizzle the glaze over the top. Allow it to set before cutting into squares.