Begin by preheating a large skillet or wok over medium-high heat.
While the skillet heats, in a small bowl, whisk together the soy sauce or coconut aminos, beef broth, erythritol, and xanthan gum (if using) until well combined. Set this sauce mixture aside.
Add two tablespoons of avocado oil to the skillet. Once hot, add the thinly sliced steak in a single layer, seasoning with salt and pepper to taste. Cook for 2-3 minutes on each side until browned and just cooked through. Remove the steak from the skillet and set aside.
In the same skillet, add the remaining tablespoon of avocado oil, followed by the broccoli florets. Stir-fry for about 3-4 minutes until the broccoli is tender yet crisp.
Push the broccoli to the sides of the skillet and add the sesame oil to the center. Add the minced garlic and grated ginger, stirring constantly for about 30 seconds, until fragrant.
Return the beef to the skillet with the broccoli. Pour the sauce mixture over the beef and broccoli, stirring to combine everything evenly.
Allow the stir-fry to simmer for 2-3 minutes until the sauce has thickened slightly and coats the beef and broccoli.
Remove from heat and, if desired, sprinkle with sesame seeds as a garnish.