Preheat the oven to 400 degrees F.
For the White Remoulade: In a food processor fitted with a metal blade, combine the egg, mustard, lemon juice, garlic and horseradish. Process until smooth. With the machine running, slowly add the oil in a steady stream until the mixture is thick. Season with salt and pepper. Cover and refrigerate until chilled.
Spread each side of the bread with the butter. Place the bread on the griddle and cook for 2 to 3 minutes on each side or until golden. Remove from the griddle. Spread each piece of the bread with the White Remoulade. Mound about 1/3 pound of the meat on each piece of bread. Lay two slices of the cheese on top of each mound of meat. Place each piece of bread on a baking sheet. Place in the oven and bake until the cheese is bubbly, about 6 to 8 minutes.
Fry the potatoes until golden brown, about 3 to 5 minutes, stirring occasionally. Remove and drain on paper towels. Season with salt and pepper. To serve, place two open-face sandwiches on each plate. Garnish each with a pile of potatoes. Garnish with the parsley.
Yield: 4 Open-Faced Sandwiches