This simplified version requires little of the labor of traditional kraut. For a more robust result, cut cored cabbage into quarters and slice crosswise into thin strips instead of shredding it.
7 cups shredded red cabbage (about 1 [2-pound] cabbage)
1 cup shredded carrot
2 1/2 tablespoons kosher salt
1 3/4 cups white vinegar
2 teaspoons caraway seeds
1 1/2 teaspoons mustard seeds
1 1/2 teaspoons black peppercorns
1/2 teaspoon whole allspice
1 cup water
1 teaspoon sugar
How to Make It
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.
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.
Rinse cabbage thoroughly under cold water. Drain cabbage; squeeze dry. Place cabbage in large bowl.
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.