Preheat the oven to 350°F (175°C). In a mixing bowl, combine mashed bananas, melted butter, sugar, egg, and vanilla extract. Mix until smooth.

In another bowl, whisk together flour, baking soda, and salt. Gradually add the dry ingredients to the banana mixture, stirring until just combined.

In a small bowl, mix together brown sugar, cinnamon, and softened butter until well combined.

On a floured surface, roll out the dough into a rectangle. Spread the cinnamon filling evenly over the dough.

Roll the dough tightly into a log, then slice into 1-inch pieces. Place the slices in a greased baking dish.

Bake in the preheated oven for 25-30 minutes or until golden brown.

While the buns are baking, prepare the icing by whisking together powdered sugar, milk, and vanilla extract until smooth.

Once baked, drizzle the icing over the warm cinnamon buns and serve immediately.