Make sure you use a flavorful mustard to coat the turkey.
Preheat oven to 425 degrees. On a rimmed baking sheet, toss carrots with 1 teaspoon oil; season with salt and pepper. Push carrots to edges of baking sheet; place turkey in center, skin side up. Coat top of turkey with mustard; season with salt and pepper. Roast until beginning to brown, 20 to 25 minutes.
In a large bowl, toss broccoli with remaining 2 teaspoons oil. Season with salt and pepper; toss broccoli with carrots on baking sheet. Continue roasting, tossing vegetables once, until turkey is browned and an instant-read thermometer inserted in center registers 165 degrees, 30 to 40 minutes.
Transfer turkey to a cutting board; tent loosely with aluminum foil, and let rest, 5 to 10 minutes. Slice turkey, and serve with vegetables, accompanied by mustard, if desired.