Bring a medium pot of water to a boil and salt it generously. Fill a medium bowl with ice water and salt it as well. Add the corn, beans, and broccoli to the boiling water and cook until crisp-tender, about 2 minutes. Use a slotted spoon or strainer to scoop out the vegetables and plunge them immediately into the ice water. Drain the vegetables, pat them dry, and add to the bowl of potatoes along with the tomatoes and cucumber. Toss the salad with 1/2 cup of the dressing. Taste, and add more salt and pepper, if desired. (The salad may be prepared up to this point 2 hours ahead and refrigerated.)
When ready to serve, toss the salad with the greens and the sprouts, if desired, and with a bit more dressing if you like your salad on the well-dressed side. Pass the remaining dressing at the table.
Yield: about 1 1/3 cups