Bring about 8 cups of water to boil in a large pot.
Combine the oyster sauce, chicken stock, Sherry, sugar and sesame oil in a small saucepan. Bring to a boil and cook until sauce thickens. Set aside.
Trim off the bottom third of the broccolini stems. If remaining stem is thick they can be cut in half lengthwise. Add broccolini to the boiling water. Once the water starts boiling again cook the greens for about 2 minutes or until the stalks are just tender. Don't overcook. Drain immediately.
Transfer to a large bowl. Pour dressing over the greens and toss well. Serve hot or allow to cool and serve at room temperature.