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For the rolls: Preheat the oven to 400 degrees F. Bring a large pot of water to a boil.
Trim the cabbage to cut away unusable outer leaves and any excess core. Place the cabbage in the water, making sure it's completely submerged, and cook for 2 to 3 minutes. Drain the cabbage and, when cool enough to touch, peel off the individual leaves. Cut away the thick vein at the base of the cabbage leaves to allow for easier rolling.
In a separate bowl add the ground beef, white rice, onions, peppers, 1 tablespoon of the red sauce, the eggs and a pinch of salt. Mix by hand until thoroughly combined. Next fill individual cabbage leaves with enough meat to fill them up without bursting out of the cabbage, about 1/2 cup per roll. Fold the sides of the cabbage in towards the meat and then roll top section of the cabbage over and around to completely encase the meat (like a burrito). Repeat for the remaining rolls.
Pour a little bit of the red sauce on the bottom of a casserole dish. Place the cabbage rolls in the casserole dish and top with the remaining red sauce. Cover the dish with foil and cook for 1 hour to 1 hour 30 minutes. Serve hot.