Pour the sesame seeds onto a baking tray. Roast the seeds in the oven for 10 to 12 minutes, until they are a rich brown around the edges.
Meanwhile, bring a large pot of salted water to a boil. Add the noodles and cook them for 5 to 6 minutes, or until they are just tender. Drain them, rinse them well with cold water, and drain them again.
In a large mixing bowl, mix together the vinegar, sugar, soy sauce, garlic, sesame oil and green onions. Add the noodles, and the toasted sesame seeds. Toss well, then stir in the broccoli. Let the dish sit for 30 minutes at room temperature before serving.