Slice the steak very thinly against the grain.
Add the beef to a bowl with the tamari (or soy sauce), cornstarch, baking soda, and avocado oil. Toss until coated and let it rest for 15–20 minutes.
Whisk together all the sauce ingredients in a small bowl and set aside.
Heat 1 tablespoon avocado oil in a large skillet over medium-high heat. Add the broccoli and water. Cook until bright green and crisp-tender. Transfer the broccoli to a plate.
Let any remaining water evaporate from the skillet. Working in two or three batches, arrange the beef in a single layer. Sear for about 1 minute, turn, and cook for another 30–60 seconds. Transfer the cooked beef to a clean plate.
Reduce the heat to medium. Whisk the sauce again, then pour it into the skillet. Cook for 1–2 minutes, stirring frequently, until bubbling, glossy, and thickened.
Return the beef, accumulated juices, and broccoli to the skillet. Toss and cook for about 1 minute, until warmed through and coated in the sauce.
Serve warm over rice with sesame seeds or sliced green onions, if desired.