Boil the cabbage. Cut the core out of the bottom of the cabbage with a paring knife, cutting about two inches deep. Submerge the whole head in a large pot of boiling water. As the outer leaves soften and loosen, peel them away with tongs and transfer them to a plate. Work through the head leaf by leaf until you have at least twelve large, intact leaves. Any torn leaves patch with smaller inner leaves folded underneath.
Preheat the oven. Set the oven to 350°F (177°C) before handling any raw meat.
Parboil the rice. Cook the rice in boiling salted water for 5 minutes only. Drain and set aside. Slightly underdone rice absorbs the tomato sauce and steams to a fully tender texture inside the sealed rolls during baking. Fully cooked rice produces a pasty, dense filling.
Brown the meat and aromatics. Cook the ground pork, ground beef, minced onions, minced garlic, dill, and parsley in a large skillet over medium-high heat until no pink remains, about 8 minutes. Drain the rendered fat from the pan before proceeding. Undrained fat turns the sauce into an oil slick during baking.
Mix the cabbage roll stuffing. Combine the browned meat mixture, parboiled rice, drained diced tomatoes, a splash of the tomato sauce, and the egg in a large bowl. Stir until evenly combined.
Prep the sauce and casserole dish. Whisk the remaining tomato sauce and condensed tomato soup together in a bowl. Spread a thin layer across the bottom of the 9x13 casserole dish to prevent the rolls from sticking.
Roll the cabbage. Cut the thick rib from the base of each leaf with a knife to make folding easier. Place two to three tablespoons of filling near the base of the leaf, fold the sides inward, and roll away from you into a compact cylinder. Place each roll seam-side down in the casserole dish. Seam-side down rolls stay closed during baking. Seam-side up rolls open and spread filling into the sauce.
Bake covered. Pour the remaining tomato sauce mixture over the tops of all the rolls. Cover the dish tightly with aluminum foil. Bake at 350°F for 75 to 90 minutes. The answer to how long to cook stuffed cabbage rolls depends on roll size: smaller rolls finish at 75 minutes, larger rolls with more filling need the full 90. Let the dish rest uncovered for 10 minutes before serving.
