Prep your veggies: Shred the cabbage, slice the green onions, and mince the garlic and ginger. Keep the green onion greens for garnish.
Warm the pan: Heat a large skillet or wok over medium-high.
Add the oil and swirl to coat.
Brown the beef: Add ground beef, breaking it up with a spatula. Cook until no pink remains and edges start to crisp, about 5–7 minutes. Do not over-stir; let it sear for flavor.
Sauté aromatics: Push the beef to one side. Add onion to the empty side and sauté 2 minutes.
Stir in garlic and ginger for 30–45 seconds until fragrant.
Add the cabbage: Toss in shredded cabbage (and carrot, if using). Stir to combine with beef and aromatics.
Season: Pour in soy sauce or tamari, rice vinegar, sesame oil, and sriracha if using. Sprinkle with black pepper.
Stir well to coat.
Cook to your texture: Let the mixture cook 4–6 minutes, stirring occasionally, until the cabbage is wilted but still crisp-tender. For softer cabbage, cook an extra 2–3 minutes.
Finish: Stir in the white parts of the green onions. Taste and adjust seasoning: add more soy for salt, vinegar for brightness, or sesame oil for nuttiness.
Garnish and serve: Remove from heat. Top with green onion greens and sesame seeds.
Serve with lime wedges if you like a little zing.