In a small bowl or measuring cup, whisk together tamari and cornstarch until smooth. Add coconut sugar, sesame oil, garlic, and ginger, and whisk to combine. Set aside.
In a mixing bowl, combine 3 tablespoons water and 2 tablespoons cornstarch to make a slurry. Add sliced beef and toss to coat evenly.
Heat 1 tablespoon avocado oil in a large cast-iron or heavy skillet over medium heat. Add broccoli florets and cook for 3–4 minutes, stirring occasionally, until bright green and fork-tender. Transfer to a plate and set aside.
Add the remaining 1 tablespoon oil to the skillet and increase heat to medium-high. Spread the beef evenly in a single layer and cook for 1½ to 2 minutes per side, until mostly cooked through.
Return the broccoli to the pan. Pour in the sauce mixture and bring to a boil, stirring frequently for 1–2 minutes until the sauce thickens and coats the beef and broccoli.
Remove from heat and serve over steamed rice. Sprinkle with sesame seeds, if desired.