Preheat oven to 350 degrees F and grease a 9×5 baking dish.
In a medium-sized bowl, whisk the flour, baking soda, cinnamon, and salt together. Set aside.
In a large bowl, beat the brown sugar and butter until creamy and then add the eggs one at a time.
Add the sour cream, mashed bananas, and vanilla to the sugar mixture and beat until combined.
Slowly add the dry ingredients to the wet ingredients until just combined. Do not overmix.
Transfer batter to the prepared loaf pan and bake for 55-60 minutes or until an inserted toothpick comes out clean. While bread is cooling, make the glaze.
In a small saucepan, combine the brown sugar and butter and bring to a boil over medium heat. Continue cooking until the sugar has fully dissolved, approximately 1 minute.
Stir in heavy cream and remove the pan from the heat. Add in the powdered sugar and salt, mix until smooth.
Allow glaze to cool for 5 minutes before pouring it over the bread.