Step 1

Prepare a large ice bath and bring a large pot of salted water to a boil. Working in batches, blanch the cabbage leaves until bright green and pliable, 1½ to 2 minutes per leaf. Shock in the ice bath and transfer to a paper towel-lined baking sheet to drain.

Step 2

In a large heavy-bottomed saucepan or Dutch oven, heat the canola oil over medium-high heat. Add half of the onion and all of the grated carrot, and cook until soft, 5 to 7 minutes. Add the tomato paste and sugar, and cook until lightly caramelized, 1 to 2 minutes. Add the chopped tomatoes, water and bay leaves, and cook until reduced by half, 15 to 20 minutes. Remove from the heat and season with salt to taste.

Step 3

In a large bowl, combine the ground meats, barberries (if using), parboiled rice and the remaining diced onion. Season with the salt and gently toss with your hands to mix, just until combined.

Step 4

Working with 1 cabbage leaf at time with the stem end facing toward you, place 2 heaping tablespoons of the filling into the center of the leaf. Fold the sides of cabbage over the filling, then roll up. Arrange the rolls, seam-side down, into the pot to form one even layer. Bring the pot to a simmer over medium-high heat. Reduce the heat to medium low, cover with the lid slightly ajar and simmer until the filling is cooked through, 35 to 45 minutes.

Step 5

Top the stuffed cabbage with the chopped dill and serve with sour cream and sourdough bread.