Preheat the oven to 375 degrees Fahrenheit and line or grease a muffin pan.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, salt, and cinnamon.
In another mixing bowl, combine the egg, brown sugar, vanilla extract, mashed bananas, and applesauce.
Pour the wet ingredients into the dry ingredients and gently stir until fully combined, without mixing more than necessary.
Use a cookie scoop or a spoon to fill each muffin cup about 2/3 full.
In a small mixing bowl, prepare the streusel by combining the brown sugar, flour, and cinnamon.
Use a pastry blender to cut in the butter.
Sprinkle the streusel over the muffins then bake for 20-25 minutes, until a toothpick comes out clean.
Whisk together the powdered sugar, milk, and vanilla extract to make the icing.
Once the muffins have cooked and cooled slightly, use a spoon to drizzle each muffin with the vanilla icing.
If you want to freeze the muffins, bake them and let them cool completely. Store them in a resealable plastic bag.
When you want to serve them, defrost them and make the streusel as described aboved. Sprinkle the streusel over the muffins and warm them in the oven by baking them at 300 degrees for five to ten minutes.
Prepare the icing as described above and drizzle over each muffin before serving.