Core the head of Green Cabbage and carefully peel off 12–16 whole leaves; blanch the leaves in boiling water for 3–5 minutes until pliable, then drain and cool on a tray.
Rinse the Rice and cook it until just tender (about 8–10 minutes), drain and let cool slightly.
Heat 1–2 tablespoons of Vegetable Oil in a skillet and sauté finely chopped Onion and grated Carrot until soft and translucent, about 5–7 minutes; set aside to cool a little.
In a large bowl combine the Ground Beef and Ground Pork with the cooked Rice and the sautéed vegetables; season generously with Fine Salt and Ground Black Pepper and mix until uniform.
Trim the thick vein from each cabbage leaf if needed, place a few tablespoons of filling near the base of a leaf, fold in the sides and roll up tightly to form a neat parcel; repeat until all filling is used.
Arrange the rolls seam-side down in a large, heavy-bottomed pot in a single layer (stacking is fine), packing them snugly so they won’t unravel during cooking.
For the sauce, warm another tablespoon of Vegetable Oil in a skillet, sauté any remaining chopped Onion briefly, then stir in the Tomato Paste and cook 1–2 minutes to deepen the flavor.
Add Water to the tomato mixture along with the Sour Cream, a pinch of Sugar, and a couple of Bay Leaves; season with more Fine Salt and Ground Black Pepper to taste, bring to a gentle simmer.
Pour the sauce evenly over the cabbage rolls so they are mostly submerged (add a little extra Water if necessary), cover the pot and simmer gently for 45–60 minutes until the cabbage is tender and the filling is cooked through.
Remove the Bay Leaves, transfer golubtsy to a serving platter and sprinkle with chopped Dill before serving. Enjoy warm with extra sour cream on the side if desired.
