Cook the potatoes in a steamer basket set over simmering water, covered, for 10 minutes.
Add the green beans and cook, covered, until the potatoes and beans are tender, 4 to 5 minutes. Run under cold water to cool.
In a small bowl, whisk together the oil, mustard, vinegar, and ¼ teaspoon each salt and pepper.
Divide the chicken, watercress, bell pepper, potatoes, and beans among plates. Drizzle with the dressing.