Bring a large pot of water to a boil, and boil the whole cabbage head for about 2 minutes. Remove the softened outer leaves and place the cabbage into the boiling water again until the remaining leaves are soft. Remove all leaves and set them aside.
Preheat the oven to 350 F
Make the filling: heat the olive oil in a large skillet over medium-high heat and saute the onion and garlic until translucent, about 2 minutes. Add the ground beef and turkey, and cook until no pink is left in the meat. Season with salt, pepper, dill, parsley, and oregano.
Mix in the cooked rice, diced tomatoes with juice, ⅓ cup of tomato sauce, and egg.
In a medium-sized bowl, mix the remaining tomato sauce with the condensed tomato soup.
With the help of a sharp knife, remove the thick part of the stems on the cabbage leaves and lay them flat on your work surface. Add ⅓ cup of filling to the center of each leaf, fold in the sides, and roll up.
Add a thin layer of tomato sauce to the bottom of a 9x13-inch baking dish and place the rolls seam side down.
Pour the remaining sauce over the rolls, cover with foil, and bake for 90 minutes.