Prep: 8 minutes; Cook: 11 minutes; Total time: 15 minutes.While the potatoes and beans are cooking, make the vinaigrette.
Place potatoes in a saucepan; cover with water to 3 inches above potatoes. Bring to a boil; simmer potatoes just until tender (about 8 minutes). Add string beans; simmer until beans are crisp and tender (about 3 minutes). Drain.
While potatoes cook, combine Dijon, vinegar, oil, salt, pepper, and 1 tablespoon dill; stir with a whisk. Set dressing aside.
Place shrimp and potatoes-and-bean mixture on platter; drizzle with dressing. Garnish with pecans and remaining dill.