Preheat a waffle iron. Into a large bowl, sift together flour, brown sugar, baking powder, salt, cinnamon, and nutmeg. Set aside.
To brown the butter, heat a thick-bottomed skillet on medium heat. Add the sliced butter, whisking frequently. Continue to cook the butter until melted. The butter will start to foam and browned specks will begin to form at the bottom of the pan. The butter should have a nutty aroma. Watch the butter carefully because it can go from brown to burnt quickly. Remove butter from the heat and let cool to room temperature.
In a medium bowl, whisk together egg yolks, buttermilk, brown butter, honey, and vanilla. Pour into dry ingredients; stir until just combined.
In a separate small bowl, mash the bananas with a fork; stir into batter. Using a stand mixer or hand mixer, beat egg whites until stiff but not dry. Gently fold into the batter.
Ladle the recommended amount of waffle batter onto the hot waffle iron according to the manufacturer's recommendations. Close lid; cook waffle is golden brown on both sides, about 5-6 minutes. Serve immediately or keep warm in a 200 degree F oven until ready to serve.
Serving options-fresh banana slices, honey, maple syrup, butter, or peanut butter
Note-these waffles freeze well. To freeze, place completely cooled waffles in a freezer bag and freeze. To reheat, pop the waffles in the toaster.