Prepare the cabbage. Bring a large pot of water to a gentle boil. Core the cabbage and carefully lower it into the water.
As the outer leaves soften, peel them off with tongs and set aside. Continue until you have about 16–20 pliable leaves. Trim the thick rib on each leaf so it folds easily without tearing.
Sauté aromatics. In a skillet over medium heat, warm the oil or butter.
Add the onion and a pinch of salt. Cook until translucent, 5–7 minutes. Stir in the garlic and cook 30 seconds more.
Let cool slightly.
Mix the filling. In a large bowl, combine ground pork, ground beef, rinsed rice, the cooled onion-garlic mixture, half the dill, sweet paprika, smoked paprika, thyme, salt, pepper, and the beaten egg. Mix gently until just combined. Do not overwork.
Make the sauce base. In a separate bowl or large measuring cup, whisk together crushed tomatoes, tomato paste, and broth.
Stir in remaining dill and add bay leaves.
Assemble the rolls. Lay a cabbage leaf flat, rib side down. Place 2–3 tablespoons of filling near the base. Fold the sides over the filling, then roll up snugly like a burrito.
Tuck the end underneath. Repeat with remaining leaves and filling. If you have small or torn leaves, overlap two pieces to make one roll.
Layer the pot. Scatter a handful of sauerkraut and half the chopped bacon on the bottom of a large Dutch oven or deep pot.
Arrange a layer of rolls seam side down. Top with more sauerkraut and some sauce. Continue layering rolls, sauerkraut, and sauce, finishing with sauce on top.
Sprinkle the remaining bacon over the top. Add extra broth if needed to just cover the rolls.
Slow cook. Bring to a gentle simmer on the stove. Cover, reduce heat to low, and cook 1.5 to 2 hours, checking occasionally.
Add a splash of broth if the liquid drops below the rolls. They’re done when the cabbage is very tender and the rice is cooked through.
Rest and serve. Let the pot sit off heat for 15 minutes. Remove bay leaves.
Taste the sauce and adjust salt and pepper. Serve hot with a spoonful of sauce, a dollop of sour cream, and extra dill. Polenta or crusty bread pairs perfectly.