Prepare the Cabbage Noodles: In a large skillet, heat 1 tablespoon of oil over medium heat. Add the shredded cabbage, season with salt and pepper, and cook for 5-7 minutes, or until tender. Set aside and keep warm.
Cook the Beef: Season the flank steak strips with salt and pepper. In the same pan, heat 2 tablespoons of oil over medium-high heat. Cook the steak in batches, searing each side until golden brown. Once browned, remove the steak from the skillet and set it aside.
Sauté the Vegetables: In the same skillet, add the remaining 2 tablespoons of oil. Toss in the sliced onion and sauté for 3-4 minutes, or until it becomes tender and translucent. Add the mushrooms, 1/2 teaspoon of kosher salt, and thyme, and sauté for another 4-5 minutes until the mushrooms are golden and tender. Stir in the minced garlic and cook for an additional minute.
Make the Sauce: Add the Tabasco sauce and beef broth to the skillet, stirring to combine and loosen any browned bits from the bottom. Bring to a simmer. Stir in the heavy cream and xanthan gum, whisking until the sauce begins to thicken.
Add Sour Cream and Beef: Reduce the heat to low, then stir in the sour cream until the sauce is smooth and creamy Add the cooked steak back to the skillet, stirring to coat the meat in the sauce. Let it cook for an additional 2-3 minutes, until heated through.
Serve: Divide the cabbage noodles among serving plates and top with the beef stroganoff.