Brown the meat: Heat a large skillet over medium-high heat.
Add 1 tablespoon oil, then the ground meat. Season with salt and pepper. Cook, breaking it up, until browned and no longer pink, 5–7 minutes.
Transfer to a plate if the pan is crowded.
Sauté aromatics: Add the remaining oil and the onion to the skillet. Cook 2–3 minutes until softened. Stir in garlic and cook until fragrant, about 30 seconds.
Add spices and tomato paste: Stir in smoked paprika, cumin, oregano, and red pepper flakes.
Add tomato paste if using. Cook 1 minute to bloom the spices and caramelize the paste.
Cook the cabbage: Add the sliced cabbage and a pinch of salt. Toss well to coat in the spices.
If the pan is too dry, add the broth. Cover and cook 4–5 minutes to soften.
Combine and finish: Return the browned meat to the skillet. Add butter for richness if you like.
Cook uncovered 3–5 more minutes, stirring, until the cabbage is tender but still has a slight bite.
Brighten it up: Stir in apple cider vinegar or lemon juice. Taste and adjust with more salt, pepper, or heat.
Serve: Top with chopped parsley or green onions. Add shredded cheese, sour cream, or avocado if desired.
Serve hot.