Preheat oven to 450°F. Toss together Brussels sprouts, 2 tablespoons oil, 1/2 teaspoon salt, and 1/2 teaspoon pepper in a large bowl. Transfer to a large rimmed baking sheet lined with aluminum foil. Roast at 450°F until golden and just tender when pierced with tip of a knife, about 20 minutes, stirring once after 10 minutes.
Meanwhile, whisk together vinegar, mustard, 1 tablespoon parsley, remaining 3/8 teaspoon salt, and remaining 1/4 teaspoon pepper in a large bowl. Add remaining 1/4 cup oil in a slow, steady stream, whisking constantly, until emulsified.
Add sprouts to dressing; toss to coat. Transfer to platter; sprinkle with remaining 1 tablespoon parsley.