Peel potatoes, and cut each into eighths. Place in a medium saucepan of cold salted water. Bring to a boil, and simmer until potatoes are very tender, about 8 minutes. Drain, and set aside in a bowl to cool. When cool, mash into coarse pieces with a fork or pastry cutter.
Preheat a waffle iron. Into a large bowl, sift together flour, sugar, baking soda, baking powder, and salt. Set aside.
In a medium bowl, whisk together egg yolks, buttermilk, and butter. Pour into the dry ingredients, and stir briefly, until just combined. Stir in potatoes.
In another medium bowl, beat egg whites with a hand-mixer until stiff but not dry. Fold into the batter.
Ladle about 1/3 cup batter onto each section of the waffle grid; spread batter almost to the edges. Close lid; bake until no steam emerges from waffle iron, 5 to 6 minutes.
Transfer waffles to a baking sheet; place in an oven set to low heat, about 200 degrees, while using remaining batter. Serve warm.