In a large pot, combine 4 quarts water and the salt and bring to a boil over high heat. Place 6 cabbage leaves in the pot, reduce the heat to medium-low, and cook for 3 to 4 minutes, until softened but not limp. Remove and drain on a rack or kitchen towel. Repeat with the remaining cabbage leaves. Cut the leaves lengthwise in half, removing the tough center ribs. (You will now have 24 half cabbage leaves. You will not need all, but some may tear.)
Heat 1 tablespoon of the butter in a large nonstick skillet. Sauté the onion and garlic until golden and soft. Remove from the heat.
In a bowl, combine the ground meats, rice, onion (set the skillet aside), and milk until you have a loose mixture. Season with the fennel, cumin, salt, and pepper.
Place 1 cabbage leaf on a work surface. Place 2 to 3 heaped tablespoons of the meat mixture in the center of the leaf and mold the mixture into a rough cylinder. Fold and roll the cabbage leaf over; tuck the ends of the leaf underneath. Repeat until you have used all the meat mixture.
Preheat the oven to 350°F. Grease a large baking dish with the vegetable oil.
Heat the remaining 1 tablespoon butter in the nonstick skillet. Add 4 to 6 cabbage rolls at a time, sprinkle with a little sugar, and cook until golden, 2 to 3 minutes. Transfer the cabbage rolls to the baking dish. When all the cabbage rolls are sautéed, deglaze the skillet with ½ cup water. Boil until reduced to 2 to 3 tablespoons and pour over the cabbage rolls.
Cover the baking dish and bake the cabbage rolls for 25 minutes. Let cool until just warm to the touch. Serve with the lingonberry preserves if desired.