Preheat oven to 400 degrees.
Toast caraway seeds in a dry pan over low heat, stirring frequently, for 2-3 minutes or until fragrant. Remove from pan and into a small bowl. Add black pepper, salt, cinnamon, allspice, clove and ginger. Place in a small food processor or coffee grinder and pulse until caraway seeds have been crushed. Mixture could also be placed in a resealable plastic bag, folded into a towel and crushed with light pressure from a rolling pin.
Add 2 cups of sauerkraut, removing as much liquid as possible, in the bowl of a food processor and pulse until finely chopped.
Tear half of the the rye bread slices into smaller pieces and place in a blender. Pulse until fine crumbs form. Measure resulting crumbs and repeat with more bread to make 3 cups.
In a large bowl, combine ground beef, 1 1/2 cups of the chopped sauerkraut, spice mixture, eggs, mustard, 2 cups of the bread crumbs and cheese.
Form into 1 1/2 inch meatballs. If the mixture is too soggy, add more breadcrumbs (1/2 cup at a time). If the mixture is too dry, add liquid from sauerkraut (1/4 cup at a time). Make adjustments until meatballs will hold together. Place in a roasting pan or two sheet pans that have been coated with cooking spray or lined with aluminum foil. Leave room between the meatballs to allow browning and even baking. Toss carrots, onions and celery in between the meatballs.
Bake for 10 minutes. Reduce heat to 350 degrees and bake for an additional 10 minutes. Larger meatballs may require more baking time.
Serve hot with Thousand Island Coleslaw.