Preheat a panini grill or a George Foreman grill and lightly grease it with non-stick spray (or preheat an oven to 350°F).
In a bowl whisk together the ingredients for the thousand island. Season with salt and pepper to taste. Add more relish if desired. Spread the sauce on all slices of bread or serve on the side.
To build the sandwich: place a slice of cheese on a slice of bread, followed by sauerkraut, pastrami, another slice of cheese and slice of bread. Repeat for other portions if necessary.
Place on a panini grill (or George Foreman grill) and press down. Cook until the cheese is melted and bread is crispy. (If using an oven, place the sandwich on a baking sheet and cook until the cheese is melted.)