In a bowl, whisk together the brown sugar and egg yolks until smooth. Slowly stream in the butter while whisking until combined. Stir in the mashed bananas. Add the flour, baking soda, and salt, stirring until a thicker batter comes together. Pour the batter into the greased pan. Bake for 30 to 35 minutes, or until the bars seem set in the center and are golden in color. Remove and let cool slightly.