Preheat the broiler on high. Mix together the ketchup, mayonnaise, horseradish, shallot and a few grinds of pepper in a small bowl.
Lay out half of the bread and divide the pastrami among the slices. Top with the sauerkraut, followed by the cheese. Arrange the open-faced sandwiches on a large rimmed baking sheet and broil a few inches from the element until the cheese is melted and browned in spots, about 3 minutes. Spread a generous amount of the Russian dressing on the remaining slices of bread and make sandwiches. Serve immediately.