Cut the spaghetti squash in half, length-wise and steam or bake until tender about 20 minutes. Use a spoon to scoop out the strands of squash while still warm. Place in bowl to let the squash cool.
Blanch the broccoli - Cook in hot water till bright green for short period of time. Dunk in ice water to stop cooking.
Add the remaining vegetables to the spaghetti squash in bowl. Dress the salad with the vinaigrette and mix to distribute them. Place on platter, top with broccoli, and sprinkle with grated cheese before serving.