Prep the vegetables. Thinly slice the cabbage and dice the onion. Mince the garlic.
Have everything ready—this cooks quickly once you start.
Brown the beef. Heat a large skillet over medium-high. Add the oil, then the ground beef. Break it up and cook until browned with crispy edges, about 5–7 minutes.
Spoon off excess fat if needed, leaving about a tablespoon in the pan for flavor.
Season the beef. Stir in salt, pepper, smoked paprika, and oregano. Cook 30 seconds to bloom the spices.
Add onion and garlic. Add the diced onion and cook 2–3 minutes until softened. Stir in the garlic and tomato paste, and cook 1 minute until fragrant and slightly darkened.
Cook the cabbage in batches. Add half the cabbage and toss until it wilts slightly, 2–3 minutes.
Add the remaining cabbage and continue cooking, tossing often, until tender-crisp, about 5–7 minutes.
Add soy sauce and heat. Pour in the soy sauce (or tamari) and a pinch of red pepper flakes if using. Toss to coat and cook 1–2 minutes more to bring the flavors together.
Finish with vinegar. Turn off the heat and splash in the vinegar. This brightens everything and balances the richness.
Taste and adjust. Add more salt, pepper, or soy sauce if needed.
Garnish with chopped parsley or green onions. Serve hot.