Prepare the cabbage by removing the core and shredding the leaves into thin ribbons; set aside. If using rice, have it warm and ready.
Heat a large skillet or wide Dutch oven over medium-high heat and add the olive oil. When the oil shimmers, add the diced onion and cook until soft and translucent, about 4 minutes.
Stir in the minced garlic and cook 30 seconds, then add the ground turkey. Break the meat into small pieces with a spatula and brown until no pink remains, about 6–8 minutes. Season with sea salt and black pepper while cooking.
Pour in the apple cider vinegar and scrape up any browned bits from the pan to deglaze; let it reduce for 1 minute so the flavor concentrates.
Add the diced tomatoes (with juices), tomato sauce, applesauce, cinnamon, and smoked paprika. Stir to combine and bring the mixture to a simmer.
Fold in the shredded cabbage, pressing it into the sauce so it wilts. Cover the skillet, reduce heat to low, and simmer gently for 25–30 minutes, stirring every 8–10 minutes, until the cabbage is tender and most of the liquid has reduced.
Taste and adjust seasoning with a pinch more salt or pepper if needed. If the mixture tastes a touch flat, a splash more apple cider vinegar brightens it.
Serve the unstuffed cabbage hot over cauliflower rice or regular rice, and sprinkle with chopped parsley. Leftovers keep well and deepen in flavor overnight.