Make your vinaigrette and hard-cook your eggs in the morning. When you're ready for dinner, just toss the salad and assemble the sandwiches.
In a medium bowl, whisk together mustard, vinegar, and oil. Add celery and radishes, toss, and season with salt and pepper.
Spread pesto on bread and top with prosciutto, if using, egg, and Parmesan. Drizzle with oil, sprinkle with pepper, and serve with salad.