1. Combine first 3 ingredients in a large bowl. Weigh down cabbage with a smaller bowl filled with cans. Let stand at room temperature 24 hours, tossing occasionally.
2. Bring vinegar and next 4 ingredients (through allspice) to a boil in a large saucepan; reduce heat, and simmer 5 minutes. Cover and let stand at room temperature 24 hours.
3. Rinse cabbage thoroughly under cold water. Drain cabbage; squeeze dry. Place cabbage in large bowl.
4. Strain vinegar mixture through a colander over a bowl; discard solids. Stir 1 cup water and sugar into vinegar; pour over cabbage mixture, pressing down to immerse. Cover and refrigerate 5 days. Store in an airtight container in refrigerator up to 1 week.