Make the sauce:
Whisk together the water, soy sauce, brown sugar, cornstarch, garlic, ginger, and rice vinegar in a medium bowl until combined and the sugar is dissolved. Set aside.

Cook the broccoli:
Heat 2 tablespoons of the oil in a large nonstick skillet over medium-high until shimmering. Add the broccoli and cook, stirring occasionally, until tender-crisp and blackened in spots, 6 to 7 minutes. Transfer broccoli to a large bowl; set aside.

Brown the beef and add the sauce:
Reduce the heat to medium and add the remaining 1 tablespoon of oil to the skillet. Add the ground beef and sprinkle with salt. Cook, stirring occasionally to break the meat into crumbles, until browned, about 5 minutes. Add the sauce. Bring to a simmer and cook, stirring constantly, until sauce thickens slightly and flavors meld, about 3 minutes.

Assemble and serve:
Return the broccoli to the skillet and cook, stirring constantly, until the sauce has thickened and evenly coats meat and vegetables, about 3 minutes. Top with sesame seeds and green onions (if using). Serve over steamed white rice.