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Step 1
Cook rice and boil water for cabbage. Cook your rice according to package directions. While the rice is cooking, fill a 16 qt. or larger stock pot 3/4 of the way full of water (it needs to be large enough to completely submerge one head of cabbage), along with the red wine vinegar and salt, and bring that to a boil.
Step 2
Start the sauce. Meanwhile, heat your Dutch oven (or your favorite baking dish) over medium/high heat, drizzle in the olive oil, and sauté the onions with the dried thyme and tarragon for 3 minutes. Next, add the garlic and tomato paste, stirring continuously for a couple of minutes. Tip in the crushed tomatoes, a cup of beef or chicken broth, salt, and black pepper. Add the whole peeled carrot. Bring that to a simmer on medium/high heat, then lower heat to low, cover, and continue to simmer until you are ready to assemble your rolls.
Step 3
Boil the cabbage. By now, the water for the cabbage should be boiling. Carefully place the cabbage into the boiling water, one at a time, and cook for 6-8 minutes, depending on the size of your cabbage (I like to buy two small ones so they cook more evenly and all the way through, without the outer leaves getting soggy). I use a large fine mesh strainer to remove the cabbage from the boiling water; however, two wooden spoons or something similar will work as well. Bring the water back up to a boil and repeat the process with the second head of cabbage. Set the cabbage aside to cool.
Step 4
Prepare the filling. Heat a small pan with butter and olive oil. Add the diced onion and sauté for 3 minutes, then the fresh garlic for one minute. Set aside to cool. Meanwhile, place the ground beef and ground pork sausage in a large mixing bowl (or in your KitchenAid stand mixer). Combine the meats with cooked rice, fresh parsley, thyme, and tarragon, along with the hot Hungarian paprika, salt, and black pepper.
Step 5
Prepare the cabbage. By now, your cabbage should be cool enough to handle. Take your knife and deeply cut an octagon shape into the core. This will release the cabbage leaves from the core, allowing you to separate each leaf with ease. Cut a V shape into the lowermost part of each cabbage leaf, removing the hard white center (the rib).
Step 6
Form the cabbage rolls. Place a quarter cup of the meat filling on a piece of cabbage towards the core. Fold up each side of the V, roll forward, fold the ends up, then roll forward again to seal (see the video below for a demonstration). Repeat with each piece of cabbage until the meat mixture is gone.
Step 7
Finish the sauce and assemble. Remove the sauce from the heat and check to see if it is to your preferred saltiness. Eat or discard the carrot. Transfer most of the sauce from the Dutch oven to a bowl to make room for the cabbage rolls. Spread a little sauce around the bottom and edges of the Dutch oven, create a layer of stuffed cabbage rolls, then a layer of sauce, and repeat (like lasagna). Pour the remaining cup of beef or chicken broth around the edge of the pan. SEE NOTES below for INSTANT POT instructions.
Step 8
Bake the stuffed cabbage rolls. Place the lid on your Dutch oven (or foil if using a different baking dish) and bake at three hundred fifty degrees Fahrenheit (one hundred seventy-seven degrees Celsius) for about an hour and a half. The rolls should be fork tender. Serve with extra sauce on the side, spooned from the baking dish. Enjoy!