Preheat oven to 325°F. Line a standard muffin tin with paper liners and set aside.
In a small bowl, combine oats and milk and set aside to soak for 5 minutes.
In a medium bowl, combine flour, brown sugar, baking powder, baking soda, cinnamon and salt. In a large bowl, whisk together mashed banana, melted butter, egg, and vanilla extract. Add flour mixture and oat mixture to the we ingredients and mix well. Fold in walnuts.
Portion batter evenly between muffin cups and bake until golden brown and a tester inserted into the center of a muffin comes out clean, about 25 minutes.
While the muffins cool, prepare the glaze. Melted the butter in a medium sauce pan then add brown sugar. Mix until sugar has melted and the mixture is smooth.
Remove the sugar mixture from the heat and add the vanilla extract, salt, and milk or cream; mix well. Add the powdered sugar and mix thoroughly until smooth.
Drizzle the glaze over the top of each muffin. Let sit for about 5 minutes for the glaze to set then serve.