In a small pan over medium heat, melt the butter. After the butter has melted, keep on low heat, swirling butter around until foam subsides. Butter will begin to darken and will smell slightly nutty. Keep close watch because it can burn quickly. Set aside to cool for about five minutes.
Preheat oven to 350 degrees and grease or line a 12-cup muffin tin.
In a large bowl, mix together mashed bananas, browned butter, eggs, sugar and vanilla. Beast until well combined. Add in the flour, baking soda and salt, mixing until just combined. Fold in chocolate chips or nuts, if desired. Set aside.
To make the streusel, combine the flour, sugar, brown sugar and salt. Use your fingers to rub the butter into the flour mixture until large clumps form.
Using a disher or a large spoon, divide muffin batter equally between muffin cups. Top with streusel.
Bake at 350 degrees for 23-25 minutes or until a toothpick comes out clean. Cool in tin for five minutes before removing to cool completely on wire rack.