Carefully cut as much of the core as you can out of the cabbage with a small knife. This allows water to enter the cabbage and cooks it faster. Take a pot big enough to fit the cabbage comfortably, pour boiling water to cover, add salt to taste, bring to boil and let cook slowly 10-15 minutes, or until the cabbage leaves soften. Take the cabbage out onto a dish and let cool. Save the cooking water
In a small saucepan, bring the water and rice to boil, lower the heat, stir once, cover and simmer for 18 minutes. Let cool
Preheat oven to 350 F. Cook the chopped onion in the oil or butter until soft and lightly browned. In a mixing bowl combine the rice, onion, meat and egg. Loosen the leaves carefully from the cabbage one at a time. You should have about 15 leaves. Finely chop the broken ones and the smaller inner ones, and add to the meat and rice. Add the cream or half-and-half and enough of the cooking water to make a fairly loose mixture. Season with salt, pepper and marjoram
Thin out the stems of the cabbage leaves, spread the leaves out and fill each one with a full tablespoonful of the filling. Fold the sides in and roll up the leaves around the filling. Arrange the cabbage rolls into an oiled roasting pan, baste with the butter, drizzle the syrup over the rolls and bake for 1 1/2-2 hours
Midway through the baking turn the rolls over and add the broth or water to the pan. Keep adding some cooking water into the pan, if the liquid seems to be evaporating. When cooked and nicely brown, remove the rolls from the pan. Scrape off all the bits at the bottom of the pan and strain the liquid. Add 1-2 Tbsp heavy cream to the juices and more salt, if needed. Heat and pour over the rolls. Serve with lingonberries, if available