Begin by removing any damaged outer leaves from the green cabbage. Cut the cabbage into quarters, remove the core, and slice it thinly into shreds about ¼ inch thick. Rinse the shredded cabbage thoroughly under cold water to remove dirt, then lay it out to dry.

In a medium-sized bowl, combine the beef broth, soy sauce, sugar-free sweetener, rice vinegar, and if desired, chili garlic sauce. Whisk these ingredients together until well blended, adjusting sweetness and heat to your preference. For a thicker sauce, sprinkle in xanthan gum while whisking until fully incorporated.

Heat a large skillet over medium-high heat and pour in 1 tablespoon of avocado oil. Add the ground beef to the skillet, breaking it up with a wooden spoon or spatula as it cooks. Sauté the beef for about 6 to 8 minutes, until fully browned, then drain any excess fat.

Reduce heat to medium and push the browned beef to one side of the skillet. If the pan appears dry, add the remaining tablespoon of avocado oil. Add minced garlic, grated ginger, and the white parts of the green onions to the skillet, sautéing for 30 to 60 seconds until fragrant.

Add the shredded cabbage in batches, tossing it with beef to evenly wilt. After the first batch has slightly wilted, add the remaining cabbage. Drizzle with toasted sesame oil and continue cooking for 5 to 8 minutes until tender-crisp, stirring occasionally.

Once the cabbage is cooked, stir the prepared sauce again and pour it over the beef and cabbage mixture in the skillet. Toss to ensure all ingredients are coated. Simmer for an additional 3 to 5 minutes, allowing the sauce to thicken and meld flavors.

Remove from heat when sauce reaches a glossy consistency. Stir in the green onion greens, then sprinkle with toasted sesame seeds. Add fresh cilantro or extra green onion for garnish.

Serve hot from the skillet either on its own or over low-carb bases like cauliflower rice, zucchini noodles, or shirataki noodles.