Preheat a waffle iron to medium-high heat. Preheat the oven to 200 degrees F. Peel the potatoes, then shred on a box grater. Squeeze out the excess liquid into a bowl and reserve.
Combine the shredded potatoes, butter, chives, 2 teaspoons of the potato liquid, 1/2 teaspoon salt and a few grinds of pepper.
Lightly brush the top and bottom of the waffle iron with melted butter. Pour a scant 1/2 cup of the potato batter into the waffle iron, close gently and cook until golden and crisp, 4 to 8 minutes. Keep the cooked waffles warm in the oven or covered with foil on a plate while you make the remaining waffles.
Top the waffled hash browns with smoked salmon, dollop with sour cream and sprinkle with chives.
The waffles can be frozen in resealable plastic bags for up to 1 month. Reheat in a toaster oven or 300 degrees F oven until warmed through and crisp.