Preheat oven to 425 degrees F.
In a skillet, brown 5 tbsps of butter over medium heat. Remove and allow butter to cool for about 5-10 minutes.
In a large bowl, mash bananas until smooth. Add sugars, eggs, sour cream, vanilla extract, vegetable oil, browned butter, and milk.
In a separate bowl, whisk together all-purpose flour, nutmeg, baking powder, and baking soda. Add chopped walnuts to dry ingredients.
Fold flour mixture into wet ingredients until fully incorporated.
Line a muffin pan with muffin liners and fill each tin with 2-3 tbsps of batter. Top with coarse sugar and additional walnuts. Bake for 14-16 minutes.