Heat a large skillet over medium-high heat. Add the oil, then the ground beef. Cook, breaking it up with a spatula, until browned and no longer pink, about 5–7 minutes.
Drain excess fat if needed.
Add the chopped onion. Cook 2–3 minutes until softened and fragrant. Stir in the garlic and ginger and cook 30–60 seconds, just until aromatic.
Don’t let the garlic burn.
Add the shredded carrots and cabbage. Toss well to combine with the beef mixture. Cook 4–6 minutes, stirring often, until the cabbage softens but still has a slight crunch.
In a small bowl, whisk together soy sauce, rice vinegar, sesame oil, sriracha, and brown sugar or honey.
Pour over the skillet mixture and toss to coat evenly.
Season with black pepper and a pinch of salt if needed. Taste and adjust—add more soy for salt, more vinegar for brightness, or more sriracha for heat.
Turn off the heat. Stir in most of the sliced green onions, reserving some for garnish.
Sprinkle with sesame seeds if using.
Serve hot in bowls. Top with remaining green onions and optional crunchy wonton strips or chow mein noodles for extra texture.