Bring a large pot of salted water to a boil. Carefully remove the core from the cabbage and place the whole head in the boiling water for about 5 minutes, or until the leaves are tender. Remove and let cool.

In a skillet, melt 2 tablespoons of butter over medium heat. Add the chopped onion and garlic, sauté until translucent. Add the mushrooms and cook until softened. Stir in the cooked rice, salt, pepper, and paprika. Mix well and remove from heat.

Once the cabbage is cool enough to handle, carefully peel off the leaves. Place a spoonful of the filling in the center of each leaf, fold in the sides, and roll tightly. Place the rolls seam-side down in a baking dish.

Preheat the oven to 350°F (175°C). Drizzle the remaining melted butter over the cabbage rolls. Cover the dish with foil and bake for 25 minutes. Remove the foil and bake for an additional 5 minutes to brown the tops.

Serve warm, topped with sour cream and garnished with fresh dill.