Adjust oven rack to the middle position and heat to 350°F.
Spray an 8½ x 4½-inch loaf pan with vegetable oil spray.
In a medium bowl, whisk together flour, baking soda, and salt.
In a large bowl, whisk mashed bananas, brown sugar, melted butter, and eggs until well combined.
Gently whisk in the flour mixture until just combined (batter will be lumpy).
Pour batter into the prepared pan. Sprinkle granulated sugar evenly over the top.
Bake until a toothpick inserted in the center comes out clean, about 1 hour and 5 to 1 hour and 10 minutes.
Cool in the pan for 30 minutes. Remove from the pan and cool at least another 30 minutes before slicing.
Serve warm or at room temperature. Wrap tightly to store for up to 5 days.