Bring a large pot of water to a boil. Cook broccoli in boiling water for 3 minutes or so. Cook only until just tender. You will want just a little crunch left. Drain, and transfer to a large bowl and cool.
In a small bowl, whisk together the vinegar, soy sauce, sesame oil, sugar, garlic, and sesame seeds. Pour the marinade over the broccoli. Put the whole Matilda in a Ziploc bag and shake it around. Refrigerate overnight.