How to Make It
Preheat oven to high broil with rack positioned 6 inches from heat source. Let steaks stand at room temperature 20 minutes.
Meanwhile, toss together sweet potatoes, green beans, 2 tablespoons of the oil, and ¾ teaspoon of the salt on a large rimmed baking sheet. Spread in an even layer. Place a wire rack on top.
Rub steaks evenly with remaining 1 tablespoon oil; sprinkle with 1/4 teaspoon of the pepper and remaining 3/4 teaspoon salt. Arrange on rack over vegetables. Broil in preheated oven until steaks are lightly browned on 1 side, 5 to 6 minutes. Turn steaks over; broil until lightly browned on other side and cooked to medium-rare doneness (130°F), 4 to 5 minutes. Remove wire rack from baking sheet. Transfer steaks to a cutting board; rest 10 minutes.
Meanwhile, return vegetables to oven; broil until tender, 5 to 10 minutes.
Stir together butter, thyme, lemon zest, mustard, and remaining 1/4 teaspoon pepper. Slice steak against the grain. Serve steak and vegetables alongside butter.