Prepare the cabbage head: Bring a large pot of water to a boil. Core it, lower it into the water, and blanch until the outer leaves loosen, 8–10 minutes. Lift out and cool just enough to handle, separate 18–24 leaves, trim the thick ribs flat with a knife, and finely shred the small inner leaves; set both aside.
Parboil the rice in plenty of boiling water for 5 minutes. Drain well and spread to cool.
In a large Dutch oven, heat the vegetable oil over medium heat. Add the onion and garlic and cook, stirring, until very soft and translucent, 8–10 minutes. Transfer half of this onion–garlic mixture to a large bowl for the filling; leave the rest in the pot.
Stir the tomato paste into the aromatics left in the pot and cook for 1 minute. Add the crushed tomatoes, beef stock, and bay leaves; bring to a simmer. Season the sauce with about 1 tsp of the kosher salt and 0.5 tsp black pepper; reserve the rest for the filling. Simmer gently for 10 minutes, then remove from the heat.
To the bowl with the reserved aromatics, add the ground beef, ground pork, the cooled rice, egg, sweet paprika, parsley, and the remaining seasoning. Mix gently with your hands until evenly combined without compacting.
Working with one leaf at a time, place it flat with the trimmed base toward you. Put about 3 tbsp (a scant 1/4 cup) of filling near the base, fold the sides over, and roll up into a tight cylinder. Repeat with the remaining leaves and filling to make 18–24 rolls.
Stir the shredded inner leaves into the sauce in the pot to make a bed. Nestle the rolls seam-side down in a snug single layer (a little overlap is fine). Spoon sauce from the pot over the rolls to nearly cover; if needed, add a splash of water so they are at least two-thirds submerged.
Press a piece of parchment directly on the surface, cover the pot tightly with a lid or foil, and bake until the leaves and rice are very tender and the sauce is rich, 90–110 minutes.
Rest uncovered for 15 minutes so the sauce thickens slightly. Spoon rolls and sauce onto plates and serve with sour cream.