Heat the oil in a large, deep skillet or Dutch oven over medium heat. Add the onion and a pinch of salt. Cook 3–4 minutes until softened, then stir in the garlic for 30 seconds until fragrant.
Add the ground turkey or beef.
Break it up with a spatula and cook until browned and no longer pink, about 5–7 minutes. If there’s excess fat, spoon some off, but leave a little for flavor.
Stir in the smoked paprika, oregano, thyme, red pepper flakes (if using), 1 teaspoon salt, and black pepper. Toast the spices for 30 seconds to bloom their flavor.
Add the chopped cabbage, carrot, and bell pepper.
It will look like a lot—this is normal. Toss to coat everything in the seasonings. Cook 4–5 minutes, stirring occasionally, until the cabbage starts to soften and shrink.
Pour in the crushed tomatoes, tomato sauce, broth, tomato paste, and Worcestershire.
Stir well and bring to a steady simmer.
Reduce heat to medium-low, cover, and simmer 12–15 minutes, stirring once or twice, until the cabbage is tender but not mushy. Add a splash more broth if the mixture gets too thick.
Uncover and taste. Adjust salt and pepper as needed.
Stir in 1 tablespoon vinegar to brighten. Add another tablespoon if you want more tang, like classic cabbage rolls.
Serve the bowls on their own or over cooked rice, quinoa, or cauliflower rice. Finish with chopped parsley or dill and a spoon of Greek yogurt or sour cream if you like.