Begin by browning your butter. Place butter pieces in a medium-sized saucepan (preferably not a cast iron or dark-colored one as it will be hard to see when your butter begins to change color) over medium-low heat.
Once butter has melted, increase heat to just above medium. Swirl butter frequently with a wooden spoon as the butter bubbles and pops. Once the bubbling/popping slows, the butter will begin to turn brown.
Watch the butter very carefully. Once it begins to brown and you can smell the nutty aroma of browned butter, remove from heat immediately and pour into a large heatproof bowl.
Allow browned butter to cool for at least 20 minutes before proceeding.
Once butter has cooled, preheat oven to 425F (220C) and line a muffin tin with paper liners.
Stir mashed bananas into butter and stir well. Add sugars and stir again.
Add eggs, vanilla extract, and buttermilk and stir ingredients very well. Set aside.
In a separate bowl, whisk together flour, cornstarch, baking powder, baking soda, and salt.
Add the dry ingredients to your wet batter and gently fold until ingredients are mostly combined and then stir in 1 cup of pecans (reserve 1/4 cup for top) until all ingredients are just combined -- do not over-mix this batter or your muffins could come out dense and dry.
Portion batter into prepared muffin tin, filling each liner 3/4 of the way full.
Sprinkle with remaining chopped pecans and coarse sugar, if using.
Transfer muffins to oven and bake on 425F (220C) for 10 minutes and then, without opening the oven door, reduce the temperature to 350F (175C) and bake another 6-8 minutes or until a toothpick inserted in the center comes out clean or with a few moist crumbs.
Allow to cool and enjoy!
*I like to use a potato masher to mash my bananas, but a fork will work well too. Make sure to mash them well!