Prep your veggies. Core the cabbage and chop it into bite-size pieces. Dice the onion and mince the garlic. Have everything ready before you start cooking.
Brown the beef. Heat a large, deep skillet over medium-high.
Add 1 tablespoon oil, then the ground beef. Season with salt and pepper. Cook, breaking it up, until browned and no longer pink, about 5–7 minutes.
Drain excess fat if needed, then push the meat to one side.
Sauté the aromatics. Add the remaining oil to the empty side of the pan. Stir in the onion and cook until softened, 3–4 minutes. Add garlic and cook 30 seconds until fragrant.
Mix with the beef.
Bloom the spices. Stir in smoked paprika, oregano, cumin, and red pepper flakes. Toast for 30–60 seconds to bring out the flavor.
Build the sauce. Add tomato paste and cook, stirring, for 1 minute. Pour in diced tomatoes, tomato sauce, and beef broth.
Stir well and bring to a gentle simmer.
Add the cabbage. Pile in the chopped cabbage. It will look like a lot, but it cooks down. Stir to coat the cabbage in sauce.
Cover and cook for 10 minutes, stirring once or twice.
Simmer to tender. Uncover and continue cooking 8–12 minutes, until the cabbage is tender but not mushy. If the skillet gets too dry, splash in a bit more broth or water.
Finish with acidity. Stir in the vinegar. Taste and adjust salt, pepper, and heat.
The vinegar brightens the sauce and balances the beefiness.
Garnish and serve. Sprinkle with chopped parsley. Serve as-is, or add a dollop of sour cream or a small handful of shredded mozzarella if you like it creamy.