Cook pasta according to pkg directions, adding a generous Tbsp of salt to the water. Drain pasta into a large colander and rinse well with cold water.

Stir together Dressing ingredients in a large mixing bowl. Add cooked pasta and broccoli and stir well to coat. Add cucumber, pepper, and onions, and stir again. taste and adjust seasonings, if needed. Cover and refrigerate until ready to serve. Stir again just before serving.