Preheat oven to 450°F.
Toss potatoes and scallions with 4 teaspoons oil and ¼ teaspoon each pepper and salt in a large bowl. Spread evenly on a large rimmed baking sheet. Place chicken on top; drizzle with 2 teaspoons oil and sprinkle with ¼ teaspoon each pepper and salt. Roast until an instant-read thermometer inserted into the thickest part registers 165°F and the potatoes are tender, 18 to 20 minutes.
Meanwhile, whisk the remaining 2 tablespoons oil and ¼ teaspoon pepper with vinegar, herbs, mustard and shallot in a small bowl. Serve drizzled over the chicken and vegetables.
