Set grill to medium low (on my grill this is around 300 degrees Fahrenheit)
Mix together mayonnaise, ketchup, chili sauce, and horseradish. Finely chop the pickle and add to dressing. Stir in parsley. Refrigerate until ready for use.
Mix together both meats, the egg as a binder, the Worcestershire sauce, allspice, cloves and mustard along with desired amount of salt and pepper. I prefer grinding my own allspice and cloves and it takes just a couple of each. It is important not to over work the meat and have it get tough.
Divide the meat into 6 (1/3 pound) burgers about 1 inch thick and press the centers in to prevent them from balling up on the grill.
Place on the grill approximately 5 minutes per side depending on desired doneness.
Begin warming the sauerkraut in a separate pan.
The bread should go on the grill after turning the burgers, at a low temperature area so they will toast but not burn.
Top the burger with cheese in the last 2 minutes of burger cooking time.
Remove burgers and bread; spread each slice of bread with Russian dressing and top with 1/4 cup of sauerkraut. Cover with remaining bread.