Bring a large pot of water to a boil.
Remove the entire core of the cabbage with a knife. Immerse the head in the boiling water for 10 to 15 minutes, turning occasionally. Peel off each leaf with tongs as soon as it's flexible and set them aside in a colander.
In a large bowl, combine the ground beef and pork, the diced onion, the rice, sliced scallions, chopped dill and parsley, cumin, salt and pepper. Fry a teaspoon of the mixture in a small pan and taste it, then adjust the seasoning.
Shave the thick rib off each leaf with a knife held almost flat. Place a heaping tablespoon of filling in the middle of each leaf, fold the sides over, and wrap into a snug roll.
Add 1 tbsp olive oil to a large pot over medium-high heat and sauté the sliced onion for a few minutes. Once softened, lay a handful of fresh parsley on top, then any torn or leftover cabbage leaves.
Transfer the rolls to the pot in tight layers, seam side down. Cover them with an upturned heavy plate so they can't unwrap while cooking.
Pour in enough water to just cover the rolls and add the remaining ⅓ cup olive oil.
Put the lid on and simmer on low for 60 minutes. Remove from the heat, uncover, and let it sit for 10 minutes so the broth cools.