Prepare the cabbage. Using a sharp knife, carefully cut out the tough core from the bottom of the cabbage. Bring a large pot of water to a boil. Add 1 tablespoon vinegar and 2 teaspoons each of salt and sugar, then carefully lower the cabbage into the water.
Boil the cabbage for about 10 minutes, gently peeling off the outer leaves as they soften. Transfer the leaves to a plate or tray to cool. Continue until you have at least 12 large, intact leaves. You may not need the entire cabbage.
Parboil the rice. Bring a pot of water to a boil. Add the rice and cook for about 5 minutes, until partially cooked but still firm. Drain well in a fine-mesh sieve and let cool slightly.
Cook the bacon and onions. In a skillet, cook the chopped bacon until it starts to release its fat. If your bacon is on the lean side, add 1 tablespoon of butter, then add the chopped onions and cook until softened and lightly golden. Remove from heat and let cool slightly.
In a large bowl, combine the ground meat, parboiled rice, bacon and onion mixture, fresh dill, salt, pepper, minced garlic and marjoram. Mix until evenly combined.
Prepare the baking dishes. Preheat the oven to 350°F (175°C). Line the bottoms of two 8x11-inch casserole dishes with leftover cabbage leaves.
Prepare the leaves. Lay each cabbage leaf flat and carefully shave down or cut away the thick center rib to make it easier to roll without tearing.
Fill and roll. Divide the meat mixture into 12 equal portions and shape each into a cylinder. Place one portion near the base of each cabbage leaf, fold in the sides and roll tightly, like a burrito.
Arrange 6 cabbage rolls in each dish, seam-side down. You can also use one large casserole dish as long as it fits all 12 gołąbki.
Add the broth. Mix 2½–3 cups of reserved cabbage cooking water with bouillon or Better Than Bouillon, or use prepared chicken broth. Pour the broth into the baking dishes until the liquid reaches about halfway up the cabbage rolls.
Bake. Cover the dishes tightly with aluminum foil or lids and bake for about 55 minutes, or until the cabbage is tender and the meat filling is fully cooked.
Optional step: Brown the cabbage rolls. Remove the dishes from the oven. Carefully transfer the gołąbki to a plate and pour the cooking liquid into a heatproof bowl or measuring jug. Discard the cabbage leaves lining the dishes. Grease the dishes with butter, return the cabbage rolls and lightly brush their tops with more butter. Bake uncovered for another 5–15 minutes, until lightly browned and caramelized to your liking.