Fill a large pot halfway with water and bring to a boil. Carefully lower the whole cabbage head into the pot. Cover, reduce heat to medium-low, and simmer for 7–10 minutes until the leaves are softened. Remove, drain, and cool slightly. Gently peel away 12 large outer leaves and trim the thick center vein at the base of each leaf. Set aside.
In a medium bowl, combine the tomato sauce, condensed tomato soup, paprika, oregano, salt, black pepper, and crushed red pepper. Stir until smooth and well blended. Set aside.
In a large bowl, mix together the diced andouille sausage, ground beef, cooked rice, diced onion, garlic, egg, and ½ cup of the prepared sauce. Mix until evenly combined.
Spread ½ cup of the sauce mixture evenly across the bottom of a baking dish. Place one cabbage leaf flat on a clean surface. Spoon about ½ cup of filling into the center. Fold the sides inward, then roll tightly from the base to enclose the filling. Place seam-side down in the baking dish. Repeat with remaining leaves and filling.
Pour the remaining sauce evenly over the cabbage rolls. Cover tightly with foil and bake at 350°F for 1 hour.
Remove the foil, baste the rolls with the sauce, and bake uncovered for an additional 10–12 minutes. If desired, sprinkle shredded cheese on top during the last few minutes of baking.
Let rest for 5 minutes. Garnish with chopped parsley and serve warm.