Prep cabbage. Remove the core from a large head of cabbage and discard the outer few leaves.

Boil leaves. Place the cabbage in a large pot and cover completely with water. Bring to a boil and cook for about 5 minutes.

Separate cabbage leaves. Carefully turn the cabbage over and continue cooking. As the leaves begin to soften, gently peel them away from the head. The leaves should be pliable but not mushy. Continue removing softened leaves until most of the cabbage has been cooked. Set aside to cool.

Cook rice. Cook the rice for about 12 minutes, just until it begins to soften. Do not overcook, as the rice will finish cooking in the oven. Drain and rinse under cold water, then transfer to a large mixing bowl. The rice will not be fully cooked.

Cook onions. Meanwhile, sauté the onions in 2 tablespoons of butter over medium-high heat until softened.

Cook carrots. Clean and grate the carrots. Add them to the onions along with the remaining 2 tablespoons of butter. Cook until the carrots are tender. Remove from the heat and allow the vegetables to cool slightly.

Mix up filling. In a large bowl, combine the rice, ground meat, sautéed vegetables, seasonings, dill, mayonnaise, and minced garlic. Mix until well combined.

Cut cabbage leaves. Once the cabbage leaves have cooled, trim away the thick center rib from each leaf. Depending on the size, cut the leaves into 2 or 3 sections.

Prep baking dish. Line the bottom of a roasting pan or casserole dish with any unused cabbage leaves.

Build rolls. Take a section of cabbage leaf and place a portion of the meat mixture in the center. Shape the filling into a small cone. Fold the sides of the cabbage around the filling, leaving the top slightly open.

Stack cabbage rolls. Place the cabbage roll seam-side down in the prepared baking dish. Repeat with the remaining filling and cabbage leaves until you have a complete layer.

Garnish. Remove the seeds from the red pepper and slice it into thin strips. Scatter half of the pepper strips over the cabbage rolls and top with half of the butter, cut into small pieces.

Continue layering rolls. Add the remaining cabbage rolls in a second layer. Top with the remaining pepper strips and the rest of the butter.

Cook the sauce. In a skillet, bring the ketchup to a gentle simmer. Add the sour cream, heavy cream, salt, and pepper, whisking until smooth. Stir in the broth and simmer for about 30 seconds.

Cool. Allow the sauce to cool slightly before pouring it evenly over the cabbage rolls.

Cover rolls with sauce. Cover the cabbage rolls with additional cabbage leaves to prevent the top layer from drying out or browning too quickly during baking. Discard these leaves before serving.

Bake. Cover the dish tightly with foil and bake at 375°F for 60–80 minutes, or until the cabbage rolls are tender and the top cabbage leaves are lightly browned.

Serve. Serve warm with sour cream, fresh dill, and enjoy!