Step 1

Preheat the oven to 400 degrees F. Melt 3 tablespoons butter in a pot over medium-high heat. Add the cabbage, raisins, vinegar, cider, 1/4 teaspoon allspice and 1/2 teaspoon each salt and pepper; bring to a boil. Reduce the heat and simmer, covered, 20 minutes. Uncover and simmer until the liquid is almost gone. Add salt and more vinegar to taste.

Step 2

Meanwhile, sprinkle the pork with the remaining 1/4 teaspoon allspice, 1 1/4 teaspoons salt and 1/2 teaspoon pepper. Heat the olive oil in an ovenproof skillet over medium-high heat. Brown the pork on all sides, then transfer to a roasting pan (reserve the skillet) and roast until a thermometer inserted into the meat registers 145 degrees F to 150 degrees F, 10 to 15 minutes. Transfer to a cutting board.

Step 3

Boil the broth in the skillet until reduced by one-third. Mix the flour and the remaining 1 tablespoon butter, whisk into the broth and boil 1 minute. Stir in the horseradish. Slice the pork; serve with the cabbage and sauce.