Whisk shallots, mustard and vinegar with a generous sprinkling of salt and pepper in a 2-cup measuring cup. Gradually whisk in oil in a slow, steady stream to form a thick dressing. (Can be covered and held at room temperature several hours.)
Place radishes, parsley and chopped eggs in a medium bowl. (Can be covered and refrigerated for several hours.)
When ready, toss with dressing, adjust salt, pepper and vinegar to taste, and serve.
