Start by making the stir-fry sauce; you can do this a few days ahead of time. Place the tamari or soy sauce, sesame oil, garlic, ginger, Sriracha, and honey in a mason jar, cover, and shake until the ingredients are combined. You can also whisk them together in a small bowl. Set the sauce aside.
Season the steak with salt and pepper.
Cook the steak. You'll need to cook the beef in batches, which helps the meat get a delicious sear. If you crowd the pan, the beef will steam instead of sear.
Heat one tablespoon of olive oil in a large frying pan. Once the oil is hot, add half of the beef strips to the pan. Brown the beef on both sides and cook until no longer pink, about 4-5 minutes total. After the beef cooks, remove it from the pan and set it aside—cook the rest of the beef strips and set aside.
Heat another tablespoon of olive oil over medium-high heat in the same pan and add the broccoli. Cook for 4-5 minutes until the broccoli is bright green and tender-crisp - it will continue to soften in the sauce.
In a glass bowl or measuring cup, whisk together the beef broth and cornstarch until the cornstarch dissolves.
Pour the stir-fry sauce and beef broth mixture into the pan with broccoli.
Bring to a boil and then reduce to a simmer. Let it simmer until the sauce thickens. This takes about 3-4 minutes, maybe longer.
Once the sauce begins to thicken, add in the steak strips. Toss to coat with sauce.
Let it cook for another 2-3 minutes or until hot.
Serve over brown rice and cauliflower rice, or eat it as is. Sprinkle it with green onions and sesame seeds.