Heat oven to 350°F (convection) or 375°F (conventional).
Rinse potatoes. Toss wet potatoes with 1 tablespoon salt. Spread in single layer on sheet pans. Roast until soft, about 30 minutes. Cool to room temperature.
With the back of a spatula or palm of hand, press potatoes to about 1/2-inch thick, just until skin splits. Use immediately or cover and refrigerate up to one day.
To prepare lemon vinaigrette combine lemon zest, juice and olive oil in a covered container and shake well. Season to taste with salt and pepper. Reserve for serving.
Combine Parmesan and horseradish. Heat a non-stick skillet with a thin coating of olive oil over medium heat.
Place 10 smashed potatoes in the skillet. Cook over medium heat until potatoes are golden brown on one side, 2-3 minutes.
Sprinkle 1/2 cup Parmesan mixture evenly over potatoes. Cook about 2 minutes until cheese melts and crisps on edges. Slide potatoes onto a plate. Invert into skillet to brown the other side. Cook just until cheese is crispy, watching carefully to prevent burning.
Drizzle 2-3 tablespoons lemon vinaigrette on a serving plate. Slide potatoes onto plate. Sprinkle with parsley or chives. Serve warm.