Heat the oil in a medium saucepan over medium heat. Add the onion, garlic and 1 teaspoon salt and cook, stirring occasionally, until the onion is soft but not brown, about 5 minutes. Add the cabbage, cider, vinegar, sugar, and pepper to taste. Cover and simmer until the cabbage is tender, about 20 minutes.
Mix in the jicama, beet horseradish and dill; season with salt and pepper. Cool to room temperature. Serve with grilled sausage (left).
Photograph by Rick Lew.
Recipe courtesy Duff Goldman for Food Network Magazine