In a 4-1/2-quart Dutch oven or kettle, combine cabbage, the 1/2 cup water, the apple, lemon, onion, garlic, vinegar, and caraway seed. Tie juniper berries, whole black peppercorns, and bay leaf in a 100 percent cotton cheesecloth bag; add to cabbage mixture with salt and pepper. Bring to boiling; reduce heat. Cook, uncovered, for 2 minutes. Cover and cook for 7 to 8 minutes more or until cabbage is tender. Remove lemon halves and spice bag.
Meanwhile, in a small saucepan, melt butter or margarine. Stir in flour until smooth. Add vegetable or chicken broth or water all at once. Cook and stir until thickened and bubbly. Add sugar. Cook and stir for 2 minutes more.
Pour thickened broth over cabbage; stir to combine. If you like, add more vinegar. Makes 10 servings.
Look for juniper berries in the spice section of your supermarket.