For the dressing: Combine the mayonnaise, chili sauce, sour cream, horseradish, lemon juice, sugar, Worcestershire sauce, hot sauce, smoked paprika, dill pickles and shallots in a food processor until thoroughly mixed. Do not over blend, you still want to see some texture. Season with salt and pepper. Set aside or refrigerate in a covered jar until serving time.
For the sandwich build: Combine half of the dressing with the sauerkraut and toss. Place 1 slice of cheese on a piece of bread. Pile the meat high on the cheese, top with an additional slice of cheese, some of the sauerkraut mixture and the second piece of bread. Butter the outsides of the sandwich. Heat a heavy-bottomed nonstick skillet or griddle pan over medium-low heat. Add the sandwiches, cover with a heatproof bowl and griddle until golden and gooey in the middle, 3 to 4 minutes. Flip, cover and let cook until golden all around, another 3 minutes. Serve the extra dressing on the side.
Cook's Note: I love getting a whole piece of pastrami, uncut, from Fumare's in Chicago. If you have a favorite deli, try getting a whole piece and cutting it yourself; the meat will stay nice and tender and you can mix the bark from the end cut with the meatier middle. You'll fall in love with pastrami all over again.