Remove outer cabbage leaves. Quarter cabbage. Remove core.
Chop cabbage into bite-sized pieces.
Whisk soy sauce, gochugaru, rice vinegar, honey, sesame oil, salt, and pepper. Set aside.
Heat vegetable oil in wok over high heat.
Add garlic, ginger, and white parts of green onions. Stir-fry 30 seconds until fragrant.
Add cabbage. Toss to coat with garlic and ginger.
Stir-fry 5 to 6 minutes, tossing frequently, until tender-crisp.
Pour sauce over cabbage. Toss together.
Stir-fry 1 to 2 more minutes until sauce coats cabbage.
Remove from heat. Cabbage should be slightly charred.
Stir in green parts of green onions.
Transfer to serving dish. Garnish with sesame seeds, green onions, and red pepper flakes.
Serve hot as side or over rice as main.