Step 1

Trim off the root end of the cabbage to make the base more flat. Using a small knife, cut around and down into the core (about a third of the way through the cabbage) to remove the cone-shaped core. You want to cut/scrape the entire core out so you can start to see the cabbage layers inside.

Step 2

Place the cabbage in a large pot and fill with water. Cover tightly with a lid and bring to a boil. Then keep at a moderate simmer until the leaves soften and appear more translucent, 10 to 12 minutes. Carefully drain the water and transfer the cabbage to a plate to cool.

Step 3

Meanwhile, in a small pot, combine the rice with 1 1/2 cups water and 1/4 teaspoon salt. Cover tightly with a lid and bring to a boil. Then reduce the heat to low and simmer until all the water is absorbed, 6 to 8 minutes (do not stir during cooking). Then turn the heat off and let stand covered (still without stirring) for another 10 minutes.

Step 4

Heat 3 tablespoons oil in a large high-sided skillet over medium heat. Add the onions, carrots, and mushrooms with 1/2 teaspoon salt. Cook, stirring occasionally, until the vegetables are soft and pasty, 12 to 15 minutes. Add the garlic and soy sauce, and cook for 30 more seconds. Turn the heat off.

Step 5

Place the beans in a shallow bowl and, using a fork, mash until most of them are smashed. Add to the vegetable mixture, along with the rice (reserve the rice pot) and lots of black pepper. Stir to combine and season with more salt if needed. Set the filling aside to cool.

Step 6

Place the pot where you cooked the rice over medium heat and add the remaining tablespoon of oil. Add the tomato paste and cook, stirring frequently, letting it sizzle for about 2 minutes. Add the sugar and remaining 1/2 teaspoon salt, along with 3 cups of water. Bring the mixture to a boil, then turn the heat off.

Step 7

When the cabbage is cool enough to handle, gently peel a leaf off and place flat on a work surface. Trim off the thick spine to make the leaf more flat, keeping the rest of the leaf intact. Spoon a generous heap of the filling on the bottom of the leaf. Roll the leaf over the filling, fold the edges over, and roll upward to complete the roll. Repeat with the remaining ingredients.

Step 8

The interior cabbage leaves will be too small to roll; use these to line the bottom of a large pot or Dutch oven. Carefully place the rolls on top seam-side down. Pour the tomato sauce over the rolls. The liquid should reach almost to the top; if it doesn’t, add more water to almost cover the rolls. Cover tightly with a lid and bring to a boil. Then reduce the heat to low and simmer covered for 45 minutes. Serve garnished with dill, alongside sour cream.