In a medium bowl cover brown rice with hot water and soak for 3 hours. Drain. In a 2-quart saucepan combine rice, 3 cups water, and 1 1/2 t salt. Simmer covered for 40 minutes or until the liquid is absorbed. Add the dill seed, marjoram, and 1/2 t pepper.
In a large skillet saute 1 1/2 cups chopped onion in 3 T hot vegetable oil until soft, about 6 to 8 minutes. Add paprika and garlic, continue cooking and stirring for 2 minutes. Stir in the rice mixture, eggs, bread crumbs, and parsley. Adjust seasonings to taste. Core cabbage and, in a large pot, blanch the cabbage cored-side-down in boiling salted water for 5 minutes or until it is softened. Drain. Remove 12 leaves and cut off one fourth of each leaf from the base. Arrange 1 leaf curved-side down on a square of dampened cheesecloth and place 3 T of rice mixture in the center. Wrap the leaf around the filling and twist the corners of the cheesecloth to form the leaf into a roll. Continue making rolls with remaining filling.
Chop remaining cabbage to make 3 cups and, in a large fry pan, saute with 1 cup chopped onions and 2 T vegetable oil until soft. Add tomatoes, vermouth, broth, tomato paste, sugar, 1/2 t salt and 1/4 t pepper. Simmer the mixture for 5 minutes, stirring occasionally. Adjust seasonings. Transfer cabbage-tomato sauce mixture to a large baking dish. Arrange the cabbage rolls close together in one layer on the sauce. Spoon some of the mixture over the rolls. Bake at 325 degrees F for 1 1/2 hours. Baste rolls 4 to 5 times during cooking. Let the dish cool. Cover and refrigerate overnight. Remove cheesecloth. Heat in preheated 350 degree oven for 30 minutes before serving.